diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 3a539199acd6f..61cff302e5f4d 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -44,6 +44,7 @@ Backwards incompatible API changes
 
 .. _whatsnew_0250.api_breaking.utc_offset_indexing:
 
+
 Indexing with date strings with UTC offsets
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
@@ -215,6 +216,7 @@ Other API Changes
 - :class:`DatetimeTZDtype` will now standardize pytz timezones to a common timezone instance (:issue:`24713`)
 - ``Timestamp`` and ``Timedelta`` scalars now implement the :meth:`to_numpy` method as aliases to :meth:`Timestamp.to_datetime64` and :meth:`Timedelta.to_timedelta64`, respectively. (:issue:`24653`)
 - :meth:`Timestamp.strptime` will now rise a ``NotImplementedError`` (:issue:`25016`)
+- Comparing :class:`Timestamp` with unsupported objects now returns :py:obj:`NotImplemented` instead of raising ``TypeError``. This implies that unsupported rich comparisons are delegated to the other object, and are now consistent with Python 3 behavior for ``datetime`` objects (:issue:`24011`)
 - Bug in :meth:`DatetimeIndex.snap` which didn't preserving the ``name`` of the input :class:`Index` (:issue:`25575`)
 
 .. _whatsnew_0250.deprecations:
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index bd59da3f38612..3b7eb37a0b74a 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -227,26 +227,13 @@ cdef class _Timestamp(datetime):
                     if is_datetime64_object(other):
                         other = Timestamp(other)
                     else:
-                        if op == Py_EQ:
-                            return False
-                        elif op == Py_NE:
-                            return True
-
-                        # only allow ==, != ops
-                        raise TypeError('Cannot compare type %r with type %r' %
-                                        (type(self).__name__,
-                                         type(other).__name__))
+                        return NotImplemented
                 elif is_array(other):
                     # avoid recursion error GH#15183
                     return PyObject_RichCompare(np.array([self]), other, op)
                 return PyObject_RichCompare(other, self, reverse_ops[op])
             else:
-                if op == Py_EQ:
-                    return False
-                elif op == Py_NE:
-                    return True
-                raise TypeError('Cannot compare type %r with type %r' %
-                                (type(self).__name__, type(other).__name__))
+                return NotImplemented
 
         self._assert_tzawareness_compat(other)
         return cmp_scalar(self.value, ots.value, op)
diff --git a/pandas/tests/scalar/timestamp/test_comparisons.py b/pandas/tests/scalar/timestamp/test_comparisons.py
index b0b723e66c649..2821c0a578752 100644
--- a/pandas/tests/scalar/timestamp/test_comparisons.py
+++ b/pandas/tests/scalar/timestamp/test_comparisons.py
@@ -156,3 +156,33 @@ def test_timestamp_compare_with_early_datetime(self):
         assert stamp >= datetime(1600, 1, 1)
         assert stamp < datetime(2700, 1, 1)
         assert stamp <= datetime(2700, 1, 1)
+
+
+def test_rich_comparison_with_unsupported_type():
+    # Comparisons with unsupported objects should return NotImplemented
+    # (it previously raised TypeError, see #24011)
+
+    class Inf(object):
+        def __lt__(self, o):
+            return False
+
+        def __le__(self, o):
+            return isinstance(o, Inf)
+
+        def __gt__(self, o):
+            return not isinstance(o, Inf)
+
+        def __ge__(self, o):
+            return True
+
+        def __eq__(self, o):
+            return isinstance(o, Inf)
+
+    inf = Inf()
+    timestamp = Timestamp('2018-11-30')
+
+    for left, right in [(inf, timestamp), (timestamp, inf)]:
+        assert left > right or left < right
+        assert left >= right or left <= right
+        assert not (left == right)
+        assert left != right