diff --git a/jsonschema/_validators.py b/jsonschema/_validators.py
index 874e8796..8542a879 100644
--- a/jsonschema/_validators.py
+++ b/jsonschema/_validators.py
@@ -435,23 +435,32 @@ def unevaluatedItems(validator, unevaluatedItems, instance, schema):
 def unevaluatedProperties(validator, unevaluatedProperties, instance, schema):
     if not validator.is_type(instance, "object"):
         return
-    evaluated_property_keys = find_evaluated_property_keys_by_schema(
+    evaluated_keys = find_evaluated_property_keys_by_schema(
         validator, instance, schema,
     )
-    unevaluated_property_keys = []
+    unevaluated_keys = []
     for property in instance:
-        if property not in evaluated_property_keys:
+        if property not in evaluated_keys:
             for _ in validator.descend(
                 instance[property],
                 unevaluatedProperties,
                 path=property,
                 schema_path=property,
             ):
-                unevaluated_property_keys.append(property)
-
-    if unevaluated_property_keys:
-        error = "Unevaluated properties are not allowed (%s %s unexpected)"
-        yield ValidationError(error % extras_msg(unevaluated_property_keys))
+                # FIXME: Include context for each unevaluated property
+                #        indicating why it's invalid under the subschema.
+                unevaluated_keys.append(property)
+
+    if unevaluated_keys:
+        if unevaluatedProperties is False:
+            error = "Unevaluated properties are not allowed (%s %s unexpected)"
+            yield ValidationError(error % extras_msg(unevaluated_keys))
+        else:
+            error = (
+                "Unevaluated properties are not valid under "
+                "the given schema (%s %s unevaluated and invalid)"
+            )
+            yield ValidationError(error % extras_msg(unevaluated_keys))
 
 
 def prefixItems(validator, prefixItems, instance, schema):
diff --git a/jsonschema/tests/test_validators.py b/jsonschema/tests/test_validators.py
index 12c9dc9d..8f8680a0 100644
--- a/jsonschema/tests/test_validators.py
+++ b/jsonschema/tests/test_validators.py
@@ -634,7 +634,26 @@ def test_unevaluated_items_on_invalid_type(self):
         message = self.message_for(instance="foo", schema=schema)
         self.assertEqual(message, "'foo' is not of type 'array'")
 
-    def test_unevaluated_properties(self):
+    def test_unevaluated_properties_invalid_against_subschema(self):
+        schema = {
+            "properties": {"foo": {"type": "string"}},
+            "unevaluatedProperties": {"const": 12},
+        }
+        message = self.message_for(
+            instance={
+                "foo": "foo",
+                "bar": "bar",
+                "baz": 12,
+            },
+            schema=schema,
+        )
+        self.assertEqual(
+            message,
+            "Unevaluated properties are not valid under the given schema "
+            "('bar' was unevaluated and invalid)",
+        )
+
+    def test_unevaluated_properties_disallowed(self):
         schema = {"type": "object", "unevaluatedProperties": False}
         message = self.message_for(
             instance={