diff --git a/pyomo/contrib/incidence_analysis/scc_solver.py b/pyomo/contrib/incidence_analysis/scc_solver.py
index 378647c190c..db201dccb0a 100644
--- a/pyomo/contrib/incidence_analysis/scc_solver.py
+++ b/pyomo/contrib/incidence_analysis/scc_solver.py
@@ -66,7 +66,14 @@ def generate_strongly_connected_components(
             )
         )
 
-    assert len(variables) == len(constraints)
+    if len(variables) != len(constraints):
+        nvar = len(variables)
+        ncon = len(constraints)
+        raise RuntimeError(
+            "generate_strongly_connected_components only supports systems with the"
+            f" same numbers of variables and equality constraints. Got {nvar}"
+            f" variables and {ncon} constraints."
+        )
     if igraph is None:
         igraph = IncidenceGraphInterface()
 
@@ -78,6 +85,8 @@ def generate_strongly_connected_components(
         subsets, include_fixed=include_fixed
     ):
         # TODO: How does len scale for reference-to-list?
+        # If this assert fails, it may be due to a bug in block_triangularize
+        # or generate_subsystem_block.
         assert len(block.vars) == len(block.cons)
         yield (block, inputs)
 
diff --git a/pyomo/contrib/incidence_analysis/tests/test_scc_solver.py b/pyomo/contrib/incidence_analysis/tests/test_scc_solver.py
index b75f93e4a12..ef4853d7e9a 100644
--- a/pyomo/contrib/incidence_analysis/tests/test_scc_solver.py
+++ b/pyomo/contrib/incidence_analysis/tests/test_scc_solver.py
@@ -501,5 +501,22 @@ def test_with_inequalities(self):
         self.assertEqual(m.x[3].value, 1.0)
 
 
+@unittest.skipUnless(scipy_available, "SciPy is not available")
+@unittest.skipUnless(networkx_available, "NetworkX is not available")
+class TestExceptions(unittest.TestCase):
+    def test_nonsquare_system(self):
+        m = pyo.ConcreteModel()
+        m.x = pyo.Var([1, 2], initialize=1)
+        m.eq = pyo.Constraint(expr=m.x[1] + m.x[2] == 1)
+
+        msg = "Got 2 variables and 1 constraints"
+        with self.assertRaisesRegex(RuntimeError, msg):
+            list(
+                generate_strongly_connected_components(
+                    constraints=[m.eq], variables=[m.x[1], m.x[2]]
+                )
+            )
+
+
 if __name__ == "__main__":
     unittest.main()