diff --git a/framework/doc/content/source/mfem/postprocessors/MFEMVectorBoundaryFluxIntegralPostprocessor.md b/framework/doc/content/source/mfem/postprocessors/MFEMVectorBoundaryFluxIntegralPostprocessor.md
new file mode 100644
index 000000000000..7a97f753f84d
--- /dev/null
+++ b/framework/doc/content/source/mfem/postprocessors/MFEMVectorBoundaryFluxIntegralPostprocessor.md
@@ -0,0 +1,31 @@
+# MFEMVectorBoundaryFluxIntegralPostprocessor
+
+!if! function=hasCapability('mfem')
+
+## Overview
+
+Postprocessor for calculating the integral of the flux of a vector $H^{1,d}$,
+$L^{2,d}$, $H(\mathrm{curl})$, or $H(\mathrm{div})$  conforming source variable through a given boundary surface.
+
+!equation
+(k \vec v \cdot \hat n)_{\partial\Omega}
+
+where $\vec v \in H^{1,d}$, $L^{2,d}$, $H(\mathrm{curl})$, or $H(\mathrm{div})$,
+$k$ is an optional scalar coefficient, $\partial\Omega$ is the user-specified mesh boundary,
+and $\hat n$ is the outward facing unit normal vector on the boundary. 
+If $k$ is provided as a material coefficient, it must be defined on the boundary itself, rather than on a submesh adjacent to the boundary. 
+
+## Example Input File Syntax
+
+!listing mfem/submeshes/av_magnetostatic.i block=Postprocessors/CoilCurrent
+
+!syntax parameters /Postprocessors/MFEMVectorBoundaryFluxIntegralPostprocessor
+
+!syntax inputs /Postprocessors/MFEMVectorBoundaryFluxIntegralPostprocessor
+
+!syntax children /Postprocessors/MFEMVectorBoundaryFluxIntegralPostprocessor
+
+!if-end!
+
+!else
+!include mfem/mfem_warning.md
\ No newline at end of file
diff --git a/framework/doc/content/source/mfem/postprocessors/MFEMVectorFEInnerProductIntegralPostprocessor.md b/framework/doc/content/source/mfem/postprocessors/MFEMVectorFEInnerProductIntegralPostprocessor.md
index 352585e0e031..505055e952e3 100644
--- a/framework/doc/content/source/mfem/postprocessors/MFEMVectorFEInnerProductIntegralPostprocessor.md
+++ b/framework/doc/content/source/mfem/postprocessors/MFEMVectorFEInnerProductIntegralPostprocessor.md
@@ -15,7 +15,7 @@ and $\Omega$ is the user-specified mesh subdomain.
 
 ## Example Input File Syntax
 
-!listing mfem/submeshes/av_magnetostatic.i block=Postprocessors
+!listing mfem/submeshes/av_magnetostatic.i block=Postprocessors/CoilPower
 
 !syntax parameters /Postprocessors/MFEMVectorFEInnerProductIntegralPostprocessor
 
diff --git a/framework/include/mfem/postprocessors/MFEMVectorBoundaryFluxIntegralPostprocessor.h b/framework/include/mfem/postprocessors/MFEMVectorBoundaryFluxIntegralPostprocessor.h
new file mode 100644
index 000000000000..1becca197fc9
--- /dev/null
+++ b/framework/include/mfem/postprocessors/MFEMVectorBoundaryFluxIntegralPostprocessor.h
@@ -0,0 +1,50 @@
+//* This file is part of the MOOSE framework
+//* https://mooseframework.inl.gov
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#ifdef MOOSE_MFEM_ENABLED
+
+#pragma once
+
+#include "MFEMPostprocessor.h"
+#include "MFEMBoundaryRestrictable.h"
+
+/**
+ * Compute the integral of the flux of an MFEM vector variable across a boundary,
+ * scaled by an optional scalar coefficient.
+ */
+class MFEMVectorBoundaryFluxIntegralPostprocessor : public MFEMPostprocessor,
+                                                    public MFEMBoundaryRestrictable
+{
+public:
+  static InputParameters validParams();
+
+  MFEMVectorBoundaryFluxIntegralPostprocessor(const InputParameters & parameters);
+
+  /**
+   * Evaluate integral.
+   */
+  virtual void execute() override;
+
+  /**
+   * Return the last evaluated integral value.
+   */
+  virtual PostprocessorValue getValue() const override final;
+
+private:
+  mfem::real_t _integral;
+  mfem::ParGridFunction & _var;
+  mfem::Coefficient & _scalar_coef;
+  mfem::VectorGridFunctionCoefficient _var_coef;
+  mfem::RT_FECollection _rt_fec;
+  mfem::ParFiniteElementSpace _rt_vector_fespace;
+  mfem::ParGridFunction _rt_var;
+  mfem::ParLinearForm _boundary_integrator;
+};
+
+#endif
diff --git a/framework/src/mfem/postprocessors/MFEMVectorBoundaryFluxIntegralPostprocessor.C b/framework/src/mfem/postprocessors/MFEMVectorBoundaryFluxIntegralPostprocessor.C
new file mode 100644
index 000000000000..9f609ead9c45
--- /dev/null
+++ b/framework/src/mfem/postprocessors/MFEMVectorBoundaryFluxIntegralPostprocessor.C
@@ -0,0 +1,62 @@
+//* This file is part of the MOOSE framework
+//* https://mooseframework.inl.gov
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#ifdef MOOSE_MFEM_ENABLED
+
+#include "MFEMVectorBoundaryFluxIntegralPostprocessor.h"
+#include "MFEMProblem.h"
+
+registerMooseObject("MooseApp", MFEMVectorBoundaryFluxIntegralPostprocessor);
+
+InputParameters
+MFEMVectorBoundaryFluxIntegralPostprocessor::validParams()
+{
+  InputParameters params = MFEMPostprocessor::validParams();
+  params += MFEMBoundaryRestrictable::validParams();
+  params.addClassDescription(
+      "Calculates the integral of the flux of a vector variable across a boundary.");
+  params.addParam<MFEMScalarCoefficientName>(
+      "coefficient", "1.", "Name of optional scalar coefficient to scale integrand by.");
+  params.addRequiredParam<VariableName>("variable", "Name of the vector variable.");
+  return params;
+}
+
+MFEMVectorBoundaryFluxIntegralPostprocessor::MFEMVectorBoundaryFluxIntegralPostprocessor(
+    const InputParameters & parameters)
+  : MFEMPostprocessor(parameters),
+    MFEMBoundaryRestrictable(
+        parameters, getMFEMProblem().getMFEMVariableMesh(getParam<VariableName>("variable"))),
+    _var(
+        getMFEMProblem().getProblemData().gridfunctions.GetRef(getParam<VariableName>("variable"))),
+    _scalar_coef(getScalarCoefficient("coefficient")),
+    _var_coef(&_var),
+    _rt_fec(_var.ParFESpace()->GetMaxElementOrder(), getMesh().Dimension()),
+    _rt_vector_fespace(const_cast<mfem::ParMesh *>(&getMesh()), &_rt_fec),
+    _rt_var(&_rt_vector_fespace),
+    _boundary_integrator(&_rt_vector_fespace)
+{
+  _boundary_integrator.AddBoundaryIntegrator(
+      new mfem::VectorFEBoundaryFluxLFIntegrator(_scalar_coef), getBoundaryMarkers());
+}
+
+void
+MFEMVectorBoundaryFluxIntegralPostprocessor::execute()
+{
+  _rt_var.ProjectBdrCoefficientNormal(_var_coef, getBoundaryMarkers());
+  _boundary_integrator.Assemble();
+  _integral = _boundary_integrator(_rt_var);
+}
+
+PostprocessorValue
+MFEMVectorBoundaryFluxIntegralPostprocessor::getValue() const
+{
+  return _integral;
+}
+
+#endif
diff --git a/test/tests/mfem/submeshes/av_magnetostatic.i b/test/tests/mfem/submeshes/av_magnetostatic.i
index e0f7caaef8be..f68241f89f93 100644
--- a/test/tests/mfem/submeshes/av_magnetostatic.i
+++ b/test/tests/mfem/submeshes/av_magnetostatic.i
@@ -10,7 +10,20 @@
   type = MFEMProblem
 []
 
+[SubMeshes]
+  inactive = 'fluxcut'
+  [fluxcut]
+    type = MFEMCutTransitionSubMesh
+    cut_boundary = 'MeasurementPlane'
+    block = 'TorusCore TorusSheath'
+    transition_subdomain = transition_dom
+    transition_subdomain_boundary = transition_bdr
+    closed_subdomain = coil_dom
+  []
+[]
+
 [FESpaces]
+  inactive = 'FluxFESpace'
   [HCurlFESpace]
     type = MFEMVectorFESpace
     fec_type = ND
@@ -21,6 +34,12 @@
     fec_type = RT
     fec_order = CONSTANT
   []
+  [FluxFESpace]
+    type = MFEMVectorFESpace
+    fec_type = ND
+    fec_order = FIRST
+    submesh = fluxcut
+  []
 []
 
 [Variables]
@@ -31,6 +50,7 @@
 []
 
 [AuxVariables]
+  inactive = 'flux_e_field'
   [b_field]
     type = MFEMVariable
     fespace = HDivFESpace
@@ -39,6 +59,10 @@
     type = MFEMVariable
     fespace = HCurlFESpace
   []
+  [flux_e_field]
+    type = MFEMVariable
+    fespace = FluxFESpace
+  []
 []
 
 [AuxKernels]
@@ -70,6 +94,7 @@
 []
 
 [FunctorMaterials]
+  inactive = 'ConductorBoundary'
   [Vacuum]
     type = MFEMGenericFunctorMaterial
     prop_names = reluctivity
@@ -81,6 +106,12 @@
     prop_values = 1.0
     block = 'TorusCore TorusSheath'
   []
+  [ConductorBoundary]
+    type = MFEMGenericFunctorMaterial
+    prop_names = conductivity_boundary
+    prop_values = 1.0
+    boundary = 'MeasurementPlane'
+  []
 []
 
 [Kernels]
@@ -131,15 +162,23 @@
 []
 
 [Transfers]
+  inactive = 'submesh_transfer_to_fluxsurface'
   [from_coil]
     type = MultiAppMFEMCopyTransfer
     source_variable = e_field
     variable = e_field
     from_multi_app = coil
   []
+  [submesh_transfer_to_fluxsurface]
+    type = MFEMSubMeshTransfer
+    from_variable = e_field
+    to_variable = flux_e_field
+    execute_on = TIMESTEP_END
+  []
 []
 
 [Postprocessors]
+  inactive = 'CoilCurrent'
   [CoilPower]
     type = MFEMVectorFEInnerProductIntegralPostprocessor
     coefficient = conductivity
@@ -147,6 +186,12 @@
     primal_variable = e_field
     block = 'TorusCore TorusSheath'
   []
+  [CoilCurrent]
+    type = MFEMVectorBoundaryFluxIntegralPostprocessor
+    coefficient = conductivity_boundary
+    variable = flux_e_field
+    boundary = 'MeasurementPlane'
+  []
 []
 
 [Outputs]
diff --git a/test/tests/mfem/submeshes/gold/OutputData/AVMagnetostaticClosedCoilBoundaryFluxCSV.csv b/test/tests/mfem/submeshes/gold/OutputData/AVMagnetostaticClosedCoilBoundaryFluxCSV.csv
new file mode 100644
index 000000000000..b32a9b5c8b23
--- /dev/null
+++ b/test/tests/mfem/submeshes/gold/OutputData/AVMagnetostaticClosedCoilBoundaryFluxCSV.csv
@@ -0,0 +1,3 @@
+time,CoilCurrent
+0,0
+1,-0.099634666692599
diff --git a/test/tests/mfem/submeshes/tests b/test/tests/mfem/submeshes/tests
index 587cf2120b9c..225fe484cd4c 100644
--- a/test/tests/mfem/submeshes/tests
+++ b/test/tests/mfem/submeshes/tests
@@ -45,7 +45,7 @@
     compute_devices = 'cpu cuda'
     max_parallel = 1
     recover = false
-  []  
+  []
   [MFEMGeometryCutTransitionSubMesh]
     design = 'syntax/MFEM/ClosedCoilMagnetostatic.md'
     issues = '#31404'
@@ -58,6 +58,25 @@
     recover = false
     valgrind = heavy
   []
+  [MFEMBoundaryFluxCutTransitionSubMesh]
+    design = 'MFEMVectorBoundaryFluxIntegralPostprocessor.md'
+    issues = '#32851'
+    type = CSVDiff
+    input = av_magnetostatic.i
+    cli_args = 'SubMeshes/inactive="" '
+               'FESpaces/inactive="" '
+               'AuxVariables/inactive="" '
+               'FunctorMaterials/inactive="" '
+               'Transfers/inactive="" '
+               'Postprocessors/inactive="CoilPower" '
+               'Outputs/ReportedPostprocessors/file_base=OutputData/AVMagnetostaticClosedCoilBoundaryFluxCSV'
+    csvdiff = 'OutputData/AVMagnetostaticClosedCoilBoundaryFluxCSV.csv'    
+    requirement = 'MOOSE shall have the ability to determine the flux through an internal or external MFEM boundary surface'
+    capabilities = 'mfem'
+    compute_devices = 'cpu cuda'
+    recover = false
+    valgrind = heavy
+  []
   [MFEMVacuumCutTransitionSubMesh]
     design = 'syntax/MFEM/ClosedCoilMagnetostatic.md'
     issues = '#31404'