diff --git a/src/emsarray/conventions/ugrid.py b/src/emsarray/conventions/ugrid.py
index 77eda9a..967fcfb 100644
--- a/src/emsarray/conventions/ugrid.py
+++ b/src/emsarray/conventions/ugrid.py
@@ -748,6 +748,31 @@ def has_valid_face_edge_connectivity(self) -> bool:
             )
             return False
 
+        try:
+            fill_value = data_array.encoding['_FillValue']
+        except KeyError:
+            return True
+
+        lower_bound = _get_start_index(data_array)
+        theoretical_upper_bound = self.face_count * self.max_node_count
+        actual_upper_bound = numpy.nanmax(data_array)
+
+        if lower_bound < fill_value < actual_upper_bound:
+            warnings.warn(
+                f"Got a face_edge_connectivity variable {data_array.name!r} with "
+                f"a _FillValue inside the actual index range",
+                ConventionViolationWarning,
+            )
+            return False
+
+        if lower_bound < fill_value < theoretical_upper_bound:
+            warnings.warn(
+                f"Got a face_edge_connectivity variable {data_array.name!r} with "
+                f"a _FillValue inside the theoretical index range",
+                ConventionViolationWarning,
+            )
+            return False
+
         return True
 
     @cached_property
diff --git a/tests/conventions/test_ugrid.py b/tests/conventions/test_ugrid.py
index 0da3517..f7ecc2c 100644
--- a/tests/conventions/test_ugrid.py
+++ b/tests/conventions/test_ugrid.py
@@ -924,3 +924,40 @@ def da(attrs: dict) -> xarray.DataArray:
 
     with pytest.raises(ConventionViolationError):
         _get_start_index(da({'start_index': 2}))
+
+
+def test_has_valid_face_edge_connectivity():
+    # Create dataset with face_edges
+    dataset = make_dataset(width=3, make_edges=True, make_face_coordinates=True)
+    topology = dataset.ems.topology
+    topology.mesh_variable.attrs.update({
+        'face_edge_connectivity': 'Mesh2_face_edges',
+    })
+
+    mesh2_face_edges_array = topology.face_edge_array
+
+    mesh2_face_edges = xarray.DataArray(
+        mesh2_face_edges_array,
+        dims=[topology.face_dimension, topology.max_node_dimension],
+    )
+
+    dataset = dataset.assign({
+        'Mesh2_face_edges': mesh2_face_edges,
+    })
+
+    dataset_fill_value_in_actual_range = dataset.copy()
+
+    dataset_fill_value_in_theoretical_range = dataset.copy()
+
+    # Make sure original dataset is valid
+    assert dataset.ems.topology.has_valid_face_edge_connectivity is True
+
+    dataset_fill_value_in_actual_range['Mesh2_face_edges'].encoding['_FillValue'] = 2
+
+    with pytest.warns(ConventionViolationWarning):
+        assert dataset_fill_value_in_actual_range.ems.topology.has_valid_face_edge_connectivity is not True
+
+    dataset_fill_value_in_theoretical_range['Mesh2_face_edges'].encoding['_FillValue'] = 88
+
+    with pytest.warns(ConventionViolationWarning):
+        assert dataset_fill_value_in_theoretical_range.ems.topology.has_valid_face_edge_connectivity is not True