diff --git a/xarray/core/coordinates.py b/xarray/core/coordinates.py
index 9aa64a57ff2..6415eef4667 100644
--- a/xarray/core/coordinates.py
+++ b/xarray/core/coordinates.py
@@ -635,6 +635,68 @@ def update(self, other: Mapping[Any, Any]) -> None:
 
         self._update_coords(coords, indexes)
 
+    def set_xindex(
+        self,
+        coord_names: str | Sequence[Hashable],
+        index_cls: type[Index] | None = None,
+        **options,
+    ) -> Self:
+        """Set a new, Xarray-compatible index from one or more existing
+        coordinate(s).
+
+        Parameters
+        ----------
+        coord_names : str or list
+            Name(s) of the coordinate(s) used to build the index.
+            If several names are given, their order matters.
+        index_cls : subclass of :class:`~xarray.indexes.Index`, optional
+            The type of index to create. By default, try setting
+            a ``PandasIndex`` if ``len(coord_names) == 1``,
+            otherwise a ``PandasMultiIndex``.
+        **options
+            Options passed to the index constructor.
+
+        Returns
+        -------
+        obj : Coordinates
+            Another Coordinates object with a new index.
+
+        """
+        new_obj = self._data.set_xindex(coord_names, index_cls, **options)
+
+        # TODO: remove cast once we get rid of DatasetCoordinates
+        # and DataArrayCoordinates (i.e., Dataset and DataArray encapsulate Coordinates)
+        return cast(Self, new_obj.coords)
+
+    def drop_indexes(
+        self,
+        coord_names: Hashable | Iterable[Hashable],
+        *,
+        errors: ErrorOptions = "raise",
+    ) -> Self:
+        """Drop the indexes assigned to the given coordinates.
+
+        Parameters
+        ----------
+        coord_names : hashable or iterable of hashable
+            Name(s) of the coordinate(s) for which to drop the index.
+        errors : {"raise", "ignore"}, default: "raise"
+            If 'raise', raises a ValueError error if any of the coordinates
+            passed have no index or are not in the dataset.
+            If 'ignore', no error is raised.
+
+        Returns
+        -------
+        dropped : Coordinates
+            A new Coordinates object with dropped indexes.
+
+        """
+        new_obj = self._data.drop_indexes(coord_names, errors=errors)
+
+        # TODO: remove cast once we get rid of DatasetCoordinates
+        # and DataArrayCoordinates (i.e., Dataset and DataArray encapsulate Coordinates)
+        return cast(Self, new_obj.coords)
+
     def assign(self, coords: Mapping | None = None, **coords_kwargs: Any) -> Self:
         """Assign new coordinates (and indexes) to a Coordinates object, returning
         a new object with all the original coordinates in addition to the new ones.