diff --git a/dimod/constrained/constrained.py b/dimod/constrained/constrained.py
index 86c4fc93c..e24c720db 100644
--- a/dimod/constrained/constrained.py
+++ b/dimod/constrained/constrained.py
@@ -961,7 +961,8 @@ def _from_file_legacy(cls,
             constraint_labels = set()
             for arch in zf.namelist():
                 # even on windows zip uses /
-                match = re.match("constraints/([^/]+)/", arch)
+                # rely on the fact that we have at least an lhs file
+                match = re.match("^constraints/(.+)/lhs$", arch)
                 if match is not None:
                     constraint_labels.add(match.group(1))
 
@@ -1070,11 +1071,11 @@ def from_file(cls,
             constraint_labels = set()
             for arch in zf.namelist():
                 # even on windows zip uses /
-                match = re.match("constraints/([^/]+)/", arch)
+                match = re.match("^constraints/(.+)/lhs$", arch)
                 if match is not None:
                     constraint_labels.add(match.group(1))
 
-            for constraint in constraint_labels:                
+            for constraint in constraint_labels:
                 label = deserialize_variable(json.loads(constraint))
 
                 rhs = np.frombuffer(zf.read(f"constraints/{constraint}/rhs"), np.float64)[0]
@@ -1783,7 +1784,23 @@ def to_file(self, *,
 
             for label, constraint in self.constraints.items():
                 # put everything in a constraints/label/ directory
-                lstr = json.dumps(serialize_variable(label))
+                lstr = json.dumps(serialize_variable(label), ensure_ascii=False)
+
+                if "/" in lstr:
+                    # Because of the way we do the regex in .from_file(), we actually do
+                    # support these. But it is inconsistent with the description of the file
+                    # format so we do the simpler thing and just disallow it
+                    raise ValueError("cannot serialize constraint labels containing '/'")
+
+                if "\0" in lstr:
+                    # Similarily, this actually works, but it's weird and confusing to support it
+                    # so we disallow
+                    raise ValueError("cannot serialize constraint labels containing the NULL character")
+
+                if os.sep == '\\' and os.sep in lstr:
+                    # Irritatingly, zipfile will automatically convert \ to / on windows, so we
+                    # also don't allow that
+                    raise ValueError("cannot serialize constraint labels containing '\\' on windows")
 
                 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..46317260b 100644
--- a/tests/test_constrained.py
+++ b/tests/test_constrained.py
@@ -1334,6 +1334,81 @@ 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):
+        import os
+
+        x, y = dimod.Binaries("xy")
+
+        unusual_characters = " .~;,>|😜+-&"  # not exhaustive
+
+        if os.sep == "\\":
+            with self.subTest("\\"):
+                label = "test\\test"
+                cqm = dimod.CQM()
+                cqm.add_constraint(x + y <= 5, label=label)
+                with self.assertRaises(ValueError):
+                    cqm.to_file()
+        else:
+            unusual_characters += "\\"
+
+        for char in unusual_characters:
+            with self.subTest(f"leading {char}"):
+                label = f"{char}test"
+
+                cqm = dimod.CQM()
+                cqm.add_constraint(x + y <= 5, label=label)
+                with cqm.to_file() as f:
+                    new = dimod.CQM.from_file(f)
+
+                # best we can hope for is an equivalent after a json round trip
+                self.assertEqual(list(new.constraints), [label])
+
+            with self.subTest(f"trailing {char}"):
+                label = f"test{char}"
+
+                cqm = dimod.CQM()
+                cqm.add_constraint(x + y <= 5, label=label)
+                with cqm.to_file() as f:
+                    new = dimod.CQM.from_file(f)
+
+                # best we can hope for is an equivalent after a json round trip
+                self.assertEqual(list(new.constraints), [label])
+
+            with self.subTest(f"embedded {char}"):
+                label = f"te{char}st"
+
+                cqm = dimod.CQM()
+                cqm.add_constraint(x + y <= 5, label=label)
+                with cqm.to_file() as f:
+                    new = dimod.CQM.from_file(f)
+
+                # best we can hope for is an equivalent after a json round trip
+                self.assertEqual(list(new.constraints), [label])
+
+        with self.subTest("empty label"):
+            label = f""
+
+            cqm = dimod.CQM()
+            cqm.add_constraint(x + y <= 5, label=label)
+            with cqm.to_file() as f:
+                new = dimod.CQM.from_file(f)
+
+            self.assertEqual(list(new.constraints), [label])
+
+        with self.subTest("/"):
+            label = "test/test"
+            cqm = dimod.CQM()
+            cqm.add_constraint(x + y <= 5, label=label)
+            with self.assertRaises(ValueError):
+                cqm.to_file()
+
+        with self.subTest("NULL"):
+            label = "test\0test"
+            cqm = dimod.CQM()
+            cqm.add_constraint(x + y <= 5, label=label)
+            with self.assertRaises(ValueError):
+                cqm.to_file()
+
 
 class TestSetObjective(unittest.TestCase):
     def test_bqm(self):