diff --git a/tests/draft2019-09/const.json b/tests/draft2019-09/const.json
index 29700fda..14debdd7 100644
--- a/tests/draft2019-09/const.json
+++ b/tests/draft2019-09/const.json
@@ -383,5 +383,49 @@
                 "valid": false
             }
         ]
+    },
+    {
+        "description": "characters with the same visual representation but different codepoint",
+        "schema": {
+            "$schema": "https://json-schema.org/draft/2019-09/schema",
+            "const": "μ",
+            "$comment": "U+03BC"
+        },
+        "tests": [
+            {
+                "description": "character uses the same codepoint",
+                "data": "μ",
+                "comment": "U+03BC",
+                "valid": true
+            },
+            {
+                "description": "character looks the same but uses a different codepoint",
+                "data": "µ",
+                "comment": "U+00B5",
+                "valid": false
+            }
+        ]
+    },
+    {
+        "description": "characters with the same visual representation, but different number of codepoints",
+        "schema": {
+            "$schema": "https://json-schema.org/draft/2019-09/schema",
+            "const": "ä",
+            "$comment": "U+00E4"
+        },
+        "tests": [
+            {
+                "description": "character uses the same codepoint",
+                "data": "ä",
+                "comment": "U+00E4",
+                "valid": true
+            },
+            {
+                "description": "character looks the same but uses combining marks",
+                "data": "ä",
+                "comment": "a, U+0308",
+                "valid": false
+            }
+        ]
     }
 ]
diff --git a/tests/draft2020-12/const.json b/tests/draft2020-12/const.json
index 50be86a0..72ea3f04 100644
--- a/tests/draft2020-12/const.json
+++ b/tests/draft2020-12/const.json
@@ -383,5 +383,49 @@
                 "valid": false
             }
         ]
+    },
+    {
+        "description": "characters with the same visual representation but different codepoint",
+        "schema": {
+            "$schema": "https://json-schema.org/draft/2020-12/schema",
+            "const": "μ",
+            "$comment": "U+03BC"
+        },
+        "tests": [
+            {
+                "description": "character uses the same codepoint",
+                "data": "μ",
+                "comment": "U+03BC",
+                "valid": true
+            },
+            {
+                "description": "character looks the same but uses a different codepoint",
+                "data": "µ",
+                "comment": "U+00B5",
+                "valid": false
+            }
+        ]
+    },
+    {
+        "description": "characters with the same visual representation, but different number of codepoints",
+        "schema": {
+            "$schema": "https://json-schema.org/draft/2020-12/schema",
+            "const": "ä",
+            "$comment": "U+00E4"
+        },
+        "tests": [
+            {
+                "description": "character uses the same codepoint",
+                "data": "ä",
+                "comment": "U+00E4",
+                "valid": true
+            },
+            {
+                "description": "character looks the same but uses combining marks",
+                "data": "ä",
+                "comment": "a, U+0308",
+                "valid": false
+            }
+        ]
     }
 ]
diff --git a/tests/draft4/enum.json b/tests/draft4/enum.json
index ce43acc0..f023a492 100644
--- a/tests/draft4/enum.json
+++ b/tests/draft4/enum.json
@@ -316,5 +316,47 @@
                 "valid": false
             }
         ]
+    },
+    {
+        "description": "characters with the same visual representation but different codepoint",
+        "schema": {
+            "enum": ["μ"],
+            "$comment": "U+03BC"
+        },
+        "tests": [
+            {
+                "description": "character uses the same codepoint",
+                "data": "μ",
+                "comment": "U+03BC",
+                "valid": true
+            },
+            {
+                "description": "character looks the same but uses a different codepoint",
+                "data": "µ",
+                "comment": "U+00B5",
+                "valid": false
+            }
+        ]
+    },
+    {
+        "description": "characters with the same visual representation, but different number of codepoints",
+        "schema": {
+            "enum": ["ä"],
+            "$comment": "U+00E4"
+        },
+        "tests": [
+            {
+                "description": "character uses the same codepoint",
+                "data": "ä",
+                "comment": "U+00E4",
+                "valid": true
+            },
+            {
+                "description": "character looks the same but uses combining marks",
+                "data": "ä",
+                "comment": "a, U+0308",
+                "valid": false
+            }
+        ]
     }
 ]
diff --git a/tests/draft6/const.json b/tests/draft6/const.json
index 1c2cafcc..168fff4e 100644
--- a/tests/draft6/const.json
+++ b/tests/draft6/const.json
@@ -338,5 +338,47 @@
                 "valid": false
             }
         ]
+    },
+    {
+        "description": "characters with the same visual representation but different codepoint",
+        "schema": {
+            "const": "μ",
+            "$comment": "U+03BC"
+        },
+        "tests": [
+            {
+                "description": "character uses the same codepoint",
+                "data": "μ",
+                "comment": "U+03BC",
+                "valid": true
+            },
+            {
+                "description": "character looks the same but uses a different codepoint",
+                "data": "µ",
+                "comment": "U+00B5",
+                "valid": false
+            }
+        ]
+    },
+    {
+        "description": "characters with the same visual representation, but different number of codepoints",
+        "schema": {
+            "const": "ä",
+            "$comment": "U+00E4"
+        },
+        "tests": [
+            {
+                "description": "character uses the same codepoint",
+                "data": "ä",
+                "comment": "U+00E4",
+                "valid": true
+            },
+            {
+                "description": "character looks the same but uses combining marks",
+                "data": "ä",
+                "comment": "a, U+0308",
+                "valid": false
+            }
+        ]
     }
 ]
diff --git a/tests/draft7/const.json b/tests/draft7/const.json
index 1c2cafcc..168fff4e 100644
--- a/tests/draft7/const.json
+++ b/tests/draft7/const.json
@@ -338,5 +338,47 @@
                 "valid": false
             }
         ]
+    },
+    {
+        "description": "characters with the same visual representation but different codepoint",
+        "schema": {
+            "const": "μ",
+            "$comment": "U+03BC"
+        },
+        "tests": [
+            {
+                "description": "character uses the same codepoint",
+                "data": "μ",
+                "comment": "U+03BC",
+                "valid": true
+            },
+            {
+                "description": "character looks the same but uses a different codepoint",
+                "data": "µ",
+                "comment": "U+00B5",
+                "valid": false
+            }
+        ]
+    },
+    {
+        "description": "characters with the same visual representation, but different number of codepoints",
+        "schema": {
+            "const": "ä",
+            "$comment": "U+00E4"
+        },
+        "tests": [
+            {
+                "description": "character uses the same codepoint",
+                "data": "ä",
+                "comment": "U+00E4",
+                "valid": true
+            },
+            {
+                "description": "character looks the same but uses combining marks",
+                "data": "ä",
+                "comment": "a, U+0308",
+                "valid": false
+            }
+        ]
     }
 ]
diff --git a/tests/v1/const.json b/tests/v1/const.json
index 94f41e70..711450c8 100644
--- a/tests/v1/const.json
+++ b/tests/v1/const.json
@@ -383,5 +383,49 @@
                 "valid": false
             }
         ]
+    },
+    {
+        "description": "characters with the same visual representation but different codepoint",
+        "schema": {
+            "$schema": "https://json-schema.org/v1",
+            "const": "μ",
+            "$comment": "U+03BC"
+        },
+        "tests": [
+            {
+                "description": "character uses the same codepoint",
+                "data": "μ",
+                "comment": "U+03BC",
+                "valid": true
+            },
+            {
+                "description": "character looks the same but uses a different codepoint",
+                "data": "µ",
+                "comment": "U+00B5",
+                "valid": false
+            }
+        ]
+    },
+    {
+        "description": "characters with the same visual representation, but different number of codepoints",
+        "schema": {
+            "$schema": "https://json-schema.org/v1",
+            "const": "ä",
+            "$comment": "U+00E4"
+        },
+        "tests": [
+            {
+                "description": "character uses the same codepoint",
+                "data": "ä",
+                "comment": "U+00E4",
+                "valid": true
+            },
+            {
+                "description": "character looks the same but uses combining marks",
+                "data": "ä",
+                "comment": "a, U+0308",
+                "valid": false
+            }
+        ]
     }
 ]