ENH: consistent add/sub behavior for mixed resolutions

pandas/_libs/tslibs/timedeltas.pyx

@@ -791,8 +791,19 @@ def _binary_op_method_timedeltalike(op, name):
             # e.g. if original other was timedelta64('NaT')
             return NaT
 
-        if self._reso != other._reso:
-            raise NotImplementedError
+        # We allow silent casting to the lower resolution if and only
+        #  if it is lossless.
+        try:
+            if self._reso < other._reso:
+                other = (<_Timedelta>other)._as_reso(self._reso, round_ok=False)
+            elif self._reso > other._reso:
+                self = (<_Timedelta>self)._as_reso(other._reso, round_ok=False)
+        except ValueError as err:
+            raise ValueError(
+                "Timedelta addition/subtraction with mismatched resolutions is not "
+                "allowed when casting to the lower resolution would require "
+                "lossy rounding."
+            ) from err
 
         res = op(self.value, other.value)
         if res == NPY_NAT:

pandas/_libs/tslibs/timestamps.pyx

@@ -103,6 +103,7 @@ from pandas._libs.tslibs.offsets cimport (
     to_offset,
 )
 from pandas._libs.tslibs.timedeltas cimport (
+    _Timedelta,
     delta_to_nanoseconds,
     ensure_td64ns,
     is_any_td_scalar,
@@ -384,11 +385,36 @@ 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
-            )
+            if isinstance(other, _Timedelta):
+                # TODO: share this with __sub__, Timedelta.__add__
+                # We allow silent casting to the lower resolution if and only
+                #  if it is lossless.  See also Timestamp.__sub__
+                #  and Timedelta.__add__
+                try:
+                    if self._reso < other._reso:
+                        other = (<_Timedelta>other)._as_reso(self._reso, round_ok=False)
+                    elif self._reso > other._reso:
+                        self = (<_Timestamp>self)._as_reso(other._reso, round_ok=False)
+                except ValueError as err:
+                    raise ValueError(
+                        "Timestamp addition with mismatched resolutions is not "
+                        "allowed when casting to the lower resolution would require "
+                        "lossy rounding."
+                    ) from err
+
+            try:
+                nanos = delta_to_nanoseconds(
+                    other, reso=self._reso, round_ok=False
+                )
+            except OutOfBoundsTimedelta:
+                raise
+            except ValueError as err:
+                raise ValueError(
+                    "Addition between Timestamp and Timedelta with mismatched "
+                    "resolutions is not allowed when casting to the lower "
+                    "resolution would require lossy rounding."
+                ) from err
+
             try:
                 new_value = self.value + nanos
             except OverflowError:

pandas/tests/scalar/timedelta/test_timedelta.py

@@ -231,6 +231,41 @@ def test_floordiv_numeric(self, td):
         assert res.value == td.value // 2
         assert res._reso == td._reso
 
+    def test_addsub_mismatched_reso(self, td):
+        other = Timedelta(days=1)  # can losslessly convert to other resos
+
+        result = td + other
+        assert result._reso == td._reso
+        assert result.days == td.days + 1
+
+        result = other + td
+        assert result._reso == td._reso
+        assert result.days == td.days + 1
+
+        result = td - other
+        assert result._reso == td._reso
+        assert result.days == td.days - 1
+
+        result = other - td
+        assert result._reso == td._reso
+        assert result.days == 1 - td.days
+
+        other2 = Timedelta(500)  # can't cast losslessly
+
+        msg = (
+            "Timedelta addition/subtraction with mismatched resolutions is "
+            "not allowed when casting to the lower resolution would require "
+            "lossy rounding"
+        )
+        with pytest.raises(ValueError, match=msg):
+            td + other2
+        with pytest.raises(ValueError, match=msg):
+            other2 + td
+        with pytest.raises(ValueError, match=msg):
+            td - other2
+        with pytest.raises(ValueError, match=msg):
+            other2 - td
+
 
 class TestTimedeltaUnaryOps:
     def test_invert(self):

pandas/tests/scalar/timestamp/test_timestamp.py

@@ -966,6 +966,51 @@ def test_sub_datetimelike_mismatched_reso(self, ts_tz):
             with pytest.raises(ValueError, match=msg):
                 other - ts2
 
+    def test_sub_timedeltalike_mismatched_reso(self, ts_tz):
+        # case with non-lossy rounding
+        ts = ts_tz
+
+        # choose a unit for `other` that doesn't match ts_tz's;
+        #  this construction ensures we get cases with other._reso < ts._reso
+        #  and cases with other._reso > ts._reso
+        unit = {
+            NpyDatetimeUnit.NPY_FR_us.value: "ms",
+            NpyDatetimeUnit.NPY_FR_ms.value: "s",
+            NpyDatetimeUnit.NPY_FR_s.value: "us",
+        }[ts._reso]
+        other = Timedelta(0)._as_unit(unit)
+        assert other._reso != ts._reso
+
+        result = ts + other
+        assert isinstance(result, Timestamp)
+        assert result == ts
+        assert result._reso == min(ts._reso, other._reso)
+
+        result = other + ts
+        assert isinstance(result, Timestamp)
+        assert result == ts
+        assert result._reso == min(ts._reso, other._reso)
+
+        msg = "Timestamp addition with mismatched resolutions"
+        if ts._reso < other._reso:
+            # Case where rounding is lossy
+            other2 = other + Timedelta._from_value_and_reso(1, other._reso)
+            with pytest.raises(ValueError, match=msg):
+                ts + other2
+            with pytest.raises(ValueError, match=msg):
+                other2 + ts
+        else:
+            ts2 = ts + Timedelta._from_value_and_reso(1, ts._reso)
+            with pytest.raises(ValueError, match=msg):
+                ts2 + other
+            with pytest.raises(ValueError, match=msg):
+                other + ts2
+
+        msg = "Addition between Timestamp and Timedelta with mismatched resolutions"
+        with pytest.raises(ValueError, match=msg):
+            # With a mismatched td64 as opposed to Timedelta
+            ts + np.timedelta64(1, "ns")
+
 
 class TestAsUnit:
     def test_as_unit(self):