diff --git a/dimod/constrained/constrained.py b/dimod/constrained/constrained.py
index 86c4fc93c..dbddb7e07 100644
--- a/dimod/constrained/constrained.py
+++ b/dimod/constrained/constrained.py
@@ -1785,6 +1785,16 @@ def to_file(self, *,
                 # put everything in a constraints/label/ directory
                 lstr = json.dumps(serialize_variable(label))
 
+                # We want to disallow invalid filenames. We do this via a blacklist
+                # rather than a whitelist to be as permissive as possible. If we find enough
+                # other edge cases, we can switch in the future.
+                # Also, if we find that raising an error places an undue burden on users, we can
+                # switch to a scheme where invalid names are saved as files with generic directory
+                # labels.
+                if "/" in lstr:
+                    # NULL actually passes fine because of the JSON dumps
+                    raise ValueError("Cannot serialize constraint labels containing '/'")
+
                 with zf.open(f'constraints/{lstr}/lhs', "w", force_zip64=True) as fdst:
                     constraint.lhs._into_file(fdst)
 
diff --git a/releasenotes/notes/fix-constraint-labels-and-serialization-c0eb5e410293a63c.yaml b/releasenotes/notes/fix-constraint-labels-and-serialization-c0eb5e410293a63c.yaml
new file mode 100644
index 000000000..995b0e1ef
--- /dev/null
+++ b/releasenotes/notes/fix-constraint-labels-and-serialization-c0eb5e410293a63c.yaml
@@ -0,0 +1,7 @@
+---
+fixes:
+  - |
+    Raise an exception when serializing constrained quadratic models with constraint
+    labels containing ``"/"``. Previously they would be serialized but would subsequently
+    break deserialization.
+    See `#1358 <https://github.com/dwavesystems/dimod/issues/1358>`_.
diff --git a/tests/test_constrained.py b/tests/test_constrained.py
index 54941b012..8c9d1398f 100644
--- a/tests/test_constrained.py
+++ b/tests/test_constrained.py
@@ -1334,6 +1334,34 @@ def test_unused_variable(self):
             self.assertEqual(new.lower_bound(v), cqm.lower_bound(v))
             self.assertEqual(new.upper_bound(v), cqm.upper_bound(v))
 
+    def test_unusual_constraint_labels(self):
+        x, y = dimod.Binaries("xy")
+
+        with self.subTest("/"):
+            cqm = dimod.CQM()
+            cqm.add_constraint(x + y <= 5, label="hello/world")
+            with self.assertRaises(ValueError):
+                cqm.to_file()
+
+        # NULL actually works because it's passed through JSON
+        with self.subTest("NULL"):
+            cqm = dimod.CQM()
+            cqm.add_constraint(x + y <= 5, label="hello\0world")
+            with cqm.to_file() as f:
+                new = dimod.CQM.from_file(f)
+
+            self.assertEqual(list(new.constraints), ["hello\0world"])
+
+        # a few other potentially tricky characters, not exhaustive
+        for c in ";,\\>|😜+-&":
+            with self.subTest(c):
+                cqm = dimod.CQM()
+                cqm.add_constraint(x + y <= 5, label=f"hello{c}world")
+                with cqm.to_file() as f:
+                    new = dimod.CQM.from_file(f)
+
+                self.assertEqual(list(new.constraints), [f"hello{c}world"])
+
 
 class TestSetObjective(unittest.TestCase):
     def test_bqm(self):