diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index ec8478f3fc82a..ddf8813c9f971 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -370,9 +370,6 @@ cdef class _Timestamp(ABCTimestamp):
         cdef:
             int64_t nanos = 0
 
-        if isinstance(self, _Timestamp) and self._reso != NPY_FR_ns:
-            raise NotImplementedError(self._reso)
-
         if is_any_td_scalar(other):
             if is_timedelta64_object(other):
                 other_reso = get_datetime64_unit(other)
@@ -390,20 +387,31 @@ cdef class _Timestamp(ABCTimestamp):
                     # TODO: no tests get here
                     other = ensure_td64ns(other)
 
+            # TODO: what to do with mismatched resos?
             # TODO: disallow round_ok
             nanos = delta_to_nanoseconds(
                 other, reso=self._reso, round_ok=True
             )
             try:
-                result = type(self)(self.value + nanos, tz=self.tzinfo)
+                new_value = self.value + nanos
             except OverflowError:
                 # Use Python ints
                 # Hit in test_tdi_add_overflow
-                result = type(self)(int(self.value) + int(nanos), tz=self.tzinfo)
+                new_value = int(self.value) + int(nanos)
+
+            try:
+                result = type(self)._from_value_and_reso(new_value, reso=self._reso, tz=self.tzinfo)
+            except OverflowError as err:
+                # TODO: don't hard-code nanosecond here
+                raise OutOfBoundsDatetime(f"Out of bounds nanosecond timestamp: {new_value}") from err
+
             if result is not NaT:
                 result._set_freq(self._freq)  # avoid warning in constructor
             return result
 
+        elif isinstance(self, _Timestamp) and self._reso != NPY_FR_ns:
+            raise NotImplementedError(self._reso)
+
         elif is_integer_object(other):
             raise integer_op_not_supported(self)
 
@@ -431,13 +439,16 @@ cdef class _Timestamp(ABCTimestamp):
         return NotImplemented
 
     def __sub__(self, other):
-        if isinstance(self, _Timestamp) and self._reso != NPY_FR_ns:
-            raise NotImplementedError(self._reso)
+        if other is NaT:
+            return NaT
 
-        if is_any_td_scalar(other) or is_integer_object(other):
+        elif is_any_td_scalar(other) or is_integer_object(other):
             neg_other = -other
             return self + neg_other
 
+        elif isinstance(self, _Timestamp) and self._reso != NPY_FR_ns:
+            raise NotImplementedError(self._reso)
+
         elif is_array(other):
             if other.dtype.kind in ['i', 'u']:
                 raise integer_op_not_supported(self)
@@ -450,9 +461,6 @@ cdef class _Timestamp(ABCTimestamp):
                 )
             return NotImplemented
 
-        if other is NaT:
-            return NaT
-
         # coerce if necessary if we are a Timestamp-like
         if (PyDateTime_Check(self)
                 and (PyDateTime_Check(other) or is_datetime64_object(other))):
diff --git a/pandas/tests/scalar/timestamp/test_timestamp.py b/pandas/tests/scalar/timestamp/test_timestamp.py
index 292c8f95ec2e6..5214223c3a656 100644
--- a/pandas/tests/scalar/timestamp/test_timestamp.py
+++ b/pandas/tests/scalar/timestamp/test_timestamp.py
@@ -853,6 +853,29 @@ def test_to_period(self, dt64, ts):
         alt = Timestamp(dt64)
         assert ts.to_period("D") == alt.to_period("D")
 
+    @pytest.mark.parametrize(
+        "td", [timedelta(days=4), Timedelta(days=4), np.timedelta64(4, "D")]
+    )
+    def test_addsub_timedeltalike_non_nano(self, dt64, ts, td):
+
+        result = ts - td
+        expected = Timestamp(dt64) - td
+        assert isinstance(result, Timestamp)
+        assert result._reso == ts._reso
+        assert result == expected
+
+        result = ts + td
+        expected = Timestamp(dt64) + td
+        assert isinstance(result, Timestamp)
+        assert result._reso == ts._reso
+        assert result == expected
+
+        result = td + ts
+        expected = td + Timestamp(dt64)
+        assert isinstance(result, Timestamp)
+        assert result._reso == ts._reso
+        assert result == expected
+
 
 class TestAsUnit:
     def test_as_unit(self):