diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 00d1c50780e..402a06840e2 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -37,6 +37,9 @@ New Features
 - Added the ``count`` reduction method to both :py:class:`~core.rolling.DatasetCoarsen`
   and :py:class:`~core.rolling.DataArrayCoarsen` objects. (:pull:`3500`)
   By `Deepak Cherian <https://github.com/dcherian>`_
+- :py:meth:`Dataset.swap_dims` and :py:meth:`DataArray.swap_dims`
+  now allow swapping to dimension names that don't exist yet. (:pull:`3636`)
+  By `Justus Magin <https://github.com/keewis>`_.
 - Extend :py:class:`core.accessor_dt.DatetimeAccessor` properties 
   and support `.dt` accessor for timedelta 
   via :py:class:`core.accessor_dt.TimedeltaAccessor` (:pull:`3612`)
diff --git a/xarray/core/dataarray.py b/xarray/core/dataarray.py
index 31aa4da57b2..cbd8d243385 100644
--- a/xarray/core/dataarray.py
+++ b/xarray/core/dataarray.py
@@ -1480,8 +1480,7 @@ def swap_dims(self, dims_dict: Mapping[Hashable, Hashable]) -> "DataArray":
         ----------
         dims_dict : dict-like
             Dictionary whose keys are current dimension names and whose values
-            are new names. Each value must already be a coordinate on this
-            array.
+            are new names.
 
         Returns
         -------
@@ -1504,6 +1503,13 @@ def swap_dims(self, dims_dict: Mapping[Hashable, Hashable]) -> "DataArray":
         Coordinates:
             x        (y) <U1 'a' 'b'
           * y        (y) int64 0 1
+        >>> arr.swap_dims({"x": "z"})
+        <xarray.DataArray (z: 2)>
+        array([0, 1])
+        Coordinates:
+            x        (z) <U1 'a' 'b'
+            y        (z) int64 0 1
+        Dimensions without coordinates: z
 
         See Also
         --------
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 6be06fed117..a1da99e2b9a 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -2868,8 +2868,7 @@ def swap_dims(
         ----------
         dims_dict : dict-like
             Dictionary whose keys are current dimension names and whose values
-            are new names. Each value must already be a variable in the
-            dataset.
+            are new names.
 
         Returns
         -------
@@ -2898,6 +2897,16 @@ def swap_dims(
         Data variables:
             a        (y) int64 5 7
             b        (y) float64 0.1 2.4
+        >>> ds.swap_dims({"x": "z"})
+        <xarray.Dataset>
+        Dimensions:  (z: 2)
+        Coordinates:
+            x        (z) <U1 'a' 'b'
+            y        (z) int64 0 1
+        Dimensions without coordinates: z
+        Data variables:
+            a        (z) int64 5 7
+            b        (z) float64 0.1 2.4
 
         See Also
         --------
@@ -2914,7 +2923,7 @@ def swap_dims(
                     "cannot swap from dimension %r because it is "
                     "not an existing dimension" % k
                 )
-            if self.variables[v].dims != (k,):
+            if v in self.variables and self.variables[v].dims != (k,):
                 raise ValueError(
                     "replacement dimension %r is not a 1D "
                     "variable along the old dimension %r" % (v, k)
@@ -2923,7 +2932,7 @@ def swap_dims(
         result_dims = {dims_dict.get(dim, dim) for dim in self.dims}
 
         coord_names = self._coord_names.copy()
-        coord_names.update(dims_dict.values())
+        coord_names.update({dim for dim in dims_dict.values() if dim in self.variables})
 
         variables: Dict[Hashable, Variable] = {}
         indexes: Dict[Hashable, pd.Index] = {}
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index f957316d8ac..4189c3b504a 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -1530,6 +1530,11 @@ def test_swap_dims(self):
         actual = array.swap_dims({"x": "y"})
         assert_identical(expected, actual)
 
+        array = DataArray(np.random.randn(3), {"x": list("abc")}, "x")
+        expected = DataArray(array.values, {"x": ("y", list("abc"))}, dims="y")
+        actual = array.swap_dims({"x": "y"})
+        assert_identical(expected, actual)
+
     def test_expand_dims_error(self):
         array = DataArray(
             np.random.randn(3, 4),
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 7db1911621b..9a029121a10 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -2525,6 +2525,12 @@ def test_swap_dims(self):
         with raises_regex(ValueError, "replacement dimension"):
             original.swap_dims({"x": "z"})
 
+        expected = Dataset(
+            {"y": ("u", list("abc")), "z": 42}, coords={"x": ("u", [1, 2, 3])}
+        )
+        actual = original.swap_dims({"x": "u"})
+        assert_identical(expected, actual)
+
     def test_expand_dims_error(self):
         original = Dataset(
             {