diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index dfd64dd50f213..1df5468869df5 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -1653,15 +1653,14 @@ class Timedelta(_Timedelta):
             int64_t result, unit, remainder
             ndarray[int64_t] arr
 
-        if self._reso != NPY_FR_ns:
-            raise NotImplementedError
-
         from pandas._libs.tslibs.offsets import to_offset
-        unit = to_offset(freq).nanos
+
+        to_offset(freq).nanos  # raises on non-fixed freq
+        unit = delta_to_nanoseconds(to_offset(freq), self._reso)
 
         arr = np.array([self.value], dtype="i8")
         result = round_nsint64(arr, mode, unit)[0]
-        return Timedelta(result, unit="ns")
+        return Timedelta._from_value_and_reso(result, self._reso)
 
     def round(self, freq):
         """
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index 711d10222c133..8a2810825fc1d 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -1645,10 +1645,10 @@ class Timestamp(_Timestamp):
 
     def _round(self, freq, mode, ambiguous='raise', nonexistent='raise'):
         cdef:
-            int64_t nanos = to_offset(freq).nanos
+            int64_t nanos
 
-        if self._reso != NPY_FR_ns:
-            raise NotImplementedError(self._reso)
+        to_offset(freq).nanos  # raises on non-fixed freq
+        nanos = delta_to_nanoseconds(to_offset(freq), self._reso)
 
         if self.tz is not None:
             value = self.tz_localize(None).value
@@ -1659,7 +1659,7 @@ class Timestamp(_Timestamp):
 
         # Will only ever contain 1 element for timestamp
         r = round_nsint64(value, mode, nanos)[0]
-        result = Timestamp(r, unit='ns')
+        result = Timestamp._from_value_and_reso(r, self._reso, None)
         if self.tz is not None:
             result = result.tz_localize(
                 self.tz, ambiguous=ambiguous, nonexistent=nonexistent
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index b9388c8047df9..4b1d50c23c110 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1933,7 +1933,8 @@ def _round(self, freq, mode, ambiguous, nonexistent):
 
         values = self.view("i8")
         values = cast(np.ndarray, values)
-        nanos = to_offset(freq).nanos
+        nanos = to_offset(freq).nanos  # raises on non-fixed frequencies
+        nanos = delta_to_nanoseconds(to_offset(freq), self._reso)
         result_i8 = round_nsint64(values, mode, nanos)
         result = self._maybe_mask_results(result_i8, fill_value=iNaT)
         result = result.view(self._ndarray.dtype)
diff --git a/pandas/tests/scalar/timedelta/test_timedelta.py b/pandas/tests/scalar/timedelta/test_timedelta.py
index 00072e6724a6b..99b3bbf0186bb 100644
--- a/pandas/tests/scalar/timedelta/test_timedelta.py
+++ b/pandas/tests/scalar/timedelta/test_timedelta.py
@@ -661,6 +661,22 @@ def test_round_sanity(self, val, method):
         assert np.abs((res - td).value) < nanos
         assert res.value % nanos == 0
 
+    @pytest.mark.parametrize("unit", ["ns", "us", "ms", "s"])
+    def test_round_non_nano(self, unit):
+        td = Timedelta("1 days 02:34:57")._as_unit(unit)
+
+        res = td.round("min")
+        assert res == Timedelta("1 days 02:35:00")
+        assert res._reso == td._reso
+
+        res = td.floor("min")
+        assert res == Timedelta("1 days 02:34:00")
+        assert res._reso == td._reso
+
+        res = td.ceil("min")
+        assert res == Timedelta("1 days 02:35:00")
+        assert res._reso == td._reso
+
     def test_contains(self):
         # Checking for any NaT-like objects
         # GH 13603
diff --git a/pandas/tests/scalar/timestamp/test_unary_ops.py b/pandas/tests/scalar/timestamp/test_unary_ops.py
index 4ac50e3f4e034..2146e32a437a9 100644
--- a/pandas/tests/scalar/timestamp/test_unary_ops.py
+++ b/pandas/tests/scalar/timestamp/test_unary_ops.py
@@ -148,27 +148,26 @@ def test_round_minute_freq(self, test_input, freq, expected, rounder):
         result = func(freq)
         assert result == expected
 
-    def test_ceil(self):
-        dt = Timestamp("20130101 09:10:11")
+    @pytest.mark.parametrize("unit", ["ns", "us", "ms", "s"])
+    def test_ceil(self, unit):
+        dt = Timestamp("20130101 09:10:11")._as_unit(unit)
         result = dt.ceil("D")
         expected = Timestamp("20130102")
         assert result == expected
+        assert result._reso == dt._reso
 
-    def test_floor(self):
-        dt = Timestamp("20130101 09:10:11")
+    @pytest.mark.parametrize("unit", ["ns", "us", "ms", "s"])
+    def test_floor(self, unit):
+        dt = Timestamp("20130101 09:10:11")._as_unit(unit)
         result = dt.floor("D")
         expected = Timestamp("20130101")
         assert result == expected
+        assert result._reso == dt._reso
 
     @pytest.mark.parametrize("method", ["ceil", "round", "floor"])
     @pytest.mark.parametrize(
         "unit",
-        [
-            "ns",
-            pytest.param("us", marks=pytest.mark.xfail(reason="round not implemented")),
-            pytest.param("ms", marks=pytest.mark.xfail(reason="round not implemented")),
-            pytest.param("s", marks=pytest.mark.xfail(reason="round not implemented")),
-        ],
+        ["ns", "us", "ms", "s"],
     )
     def test_round_dst_border_ambiguous(self, method, unit):
         # GH 18946 round near "fall back" DST
@@ -203,12 +202,7 @@ def test_round_dst_border_ambiguous(self, method, unit):
     )
     @pytest.mark.parametrize(
         "unit",
-        [
-            "ns",
-            pytest.param("us", marks=pytest.mark.xfail(reason="round not implemented")),
-            pytest.param("ms", marks=pytest.mark.xfail(reason="round not implemented")),
-            pytest.param("s", marks=pytest.mark.xfail(reason="round not implemented")),
-        ],
+        ["ns", "us", "ms", "s"],
     )
     def test_round_dst_border_nonexistent(self, method, ts_str, freq, unit):
         # GH 23324 round near "spring forward" DST