diff --git a/openff/interchange/_tests/unit_tests/smirnoff/test_nonbonded.py b/openff/interchange/_tests/unit_tests/smirnoff/test_nonbonded.py
index fe3af8bf1..c39477f40 100644
--- a/openff/interchange/_tests/unit_tests/smirnoff/test_nonbonded.py
+++ b/openff/interchange/_tests/unit_tests/smirnoff/test_nonbonded.py
@@ -160,6 +160,30 @@ def test_nonstandard_scale_factors(
             for index, factor in factors.items():
                 assert getattr(interchange[collection], f"scale1{index}") == factor
 
+    @pytest.mark.skip("Behavior not implemented yet")
+    def test_nagl_charges_fails_fallback(self, sage_with_nagl_charges):
+        """Test whether molecules that fail having charges assigned by NAGLCharges successfully
+        fall back to lower-precedence charge methods
+        """
+        # Create a molecule that NAGL can't charge
+        mol = Molecule.from_smiles("B")
+        # Create a FF with a ChargeIncrementModel that CAN charge the molecule
+        sage_with_nagl_charges.deregister_parameter_handler("Bonds")
+        sage_with_nagl_charges.deregister_parameter_handler("Constraints")
+        sage_with_nagl_charges.deregister_parameter_handler("Angles")
+        sage_with_nagl_charges.deregister_parameter_handler("ProperTorsions")
+        sage_with_nagl_charges.deregister_parameter_handler("ImproperTorsions")
+        sage_with_nagl_charges.deregister_parameter_handler("vdW")
+        sage_with_nagl_charges.get_parameter_handler(
+            "ChargeIncrementModel",
+            {
+                "partial_charge_method": "formal_charge",
+                "version": "0.3",
+            },
+        )
+        # Ensure that no error is raised when assigning charges, since NAGL will fail but CIMH will succeed
+        sage_with_nagl_charges.create_interchange(mol.to_topology())
+
 
 class TestvdWUpDownConversion:
     def test_upconversion(self):
diff --git a/openff/interchange/smirnoff/_nonbonded.py b/openff/interchange/smirnoff/_nonbonded.py
index e97d5f55e..1b32d9496 100644
--- a/openff/interchange/smirnoff/_nonbonded.py
+++ b/openff/interchange/smirnoff/_nonbonded.py
@@ -744,7 +744,7 @@ def _find_reference_matches(
         potentials: dict[PotentialKey, Potential] = dict()
 
         expected_matches = {i for i in range(unique_molecule.n_atoms)}
-
+        exceptions = []
         for handler_type in cls.parameter_handler_precedence():
             if handler_type not in parameter_handlers:
                 continue
@@ -761,15 +761,19 @@ def _find_reference_matches(
                     unique_molecule,
                 )
 
-            if handler_type in ["ToolkitAM1BCC", "ChargeIncrementModel"]:
-                (
-                    partial_charge_method,
-                    am1_matches,
-                    am1_potentials,
-                ) = cls._find_charge_model_matches(
-                    parameter_handler,
-                    unique_molecule,
-                )
+            if handler_type in ["ToolkitAM1BCC", "ChargeIncrementModel", "NAGLCharges"]:
+                try:
+                    (
+                        partial_charge_method,
+                        am1_matches,
+                        am1_potentials,
+                    ) = cls._find_charge_model_matches(
+                        parameter_handler,
+                        unique_molecule,
+                    )
+                except ValueError as e:
+                    exceptions.append(e)
+                    continue
 
             if slot_matches is None and am1_matches is None:
                 raise NotImplementedError()
@@ -813,10 +817,13 @@ def _find_reference_matches(
         found_matches = {index for key in matches for index in key.atom_indices}
 
         if found_matches != expected_matches:
+            exceptions_txt = "\n\n\n".join([str(i) for i in exceptions])
+
             raise RuntimeError(
                 f"{unique_molecule.to_smiles(explicit_hydrogens=False)} could "
                 "not be fully assigned charges. Charges were assigned to atoms "
-                f"{found_matches} but the molecule contains {expected_matches}.",
+                f"{found_matches} but the molecule contains {expected_matches}."
+                f"\n\n{exceptions_txt}",
             )
 
         return matches, potentials