diff --git a/lib/matplotlib/backends/backend_agg.py b/lib/matplotlib/backends/backend_agg.py
index 0fe0fc40c00b..47892aacd425 100644
--- a/lib/matplotlib/backends/backend_agg.py
+++ b/lib/matplotlib/backends/backend_agg.py
@@ -441,7 +441,9 @@ def buffer_rgba(self):
         """
         return self.renderer.buffer_rgba()
 
-    def print_raw(self, filename_or_obj):
+    def print_raw(self, filename_or_obj, *, metadata=None):
+        if metadata is not None:
+            raise ValueError("metadata not supported for raw/rgba")
         FigureCanvasAgg.draw(self)
         renderer = self.get_renderer()
         with cbook.open_file_cm(filename_or_obj, "wb") as fh:
@@ -518,22 +520,22 @@ def print_to_buffer(self):
     # print_figure(), and the latter ensures that `self.figure.dpi` already
     # matches the dpi kwarg (if any).
 
-    def print_jpg(self, filename_or_obj, *, pil_kwargs=None):
+    def print_jpg(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
         # savefig() has already applied savefig.facecolor; we now set it to
         # white to make imsave() blend semi-transparent figures against an
         # assumed white background.
         with mpl.rc_context({"savefig.facecolor": "white"}):
-            self._print_pil(filename_or_obj, "jpeg", pil_kwargs)
+            self._print_pil(filename_or_obj, "jpeg", pil_kwargs, metadata)
 
     print_jpeg = print_jpg
 
-    def print_tif(self, filename_or_obj, *, pil_kwargs=None):
-        self._print_pil(filename_or_obj, "tiff", pil_kwargs)
+    def print_tif(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
+        self._print_pil(filename_or_obj, "tiff", pil_kwargs, metadata)
 
     print_tiff = print_tif
 
-    def print_webp(self, filename_or_obj, *, pil_kwargs=None):
-        self._print_pil(filename_or_obj, "webp", pil_kwargs)
+    def print_webp(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
+        self._print_pil(filename_or_obj, "webp", pil_kwargs, metadata)
 
     print_jpg.__doc__, print_tif.__doc__, print_webp.__doc__ = map(
         """
diff --git a/lib/matplotlib/figure.py b/lib/matplotlib/figure.py
index d2568fddbf06..00df76d344a2 100644
--- a/lib/matplotlib/figure.py
+++ b/lib/matplotlib/figure.py
@@ -3259,6 +3259,11 @@ def savefig(self, fname, *, transparent=None, **kwargs):
               `~.FigureCanvasSVG.print_svg`.
             - 'eps' and 'ps' with PS backend: Only 'Creator' is supported.
 
+            Not supported for 'pgf', 'raw', and 'rgba' as those formats do not support
+            embedding metadata.
+            Does not currently support 'jpg', 'tiff', or 'webp', but may include
+            embedding EXIF metadata in the future.
+
         bbox_inches : str or `.Bbox`, default: :rc:`savefig.bbox`
             Bounding box in inches: only the given portion of the figure is
             saved.  If 'tight', try to figure out the tight bbox of the figure.
diff --git a/lib/matplotlib/image.py b/lib/matplotlib/image.py
index 495f131a1b24..373197aa0aea 100644
--- a/lib/matplotlib/image.py
+++ b/lib/matplotlib/image.py
@@ -1610,6 +1610,7 @@ def imsave(fname, arr, vmin=None, vmax=None, cmap=None, format=None,
         Metadata in the image file.  The supported keys depend on the output
         format, see the documentation of the respective backends for more
         information.
+        Currently only supported for "png", "pdf", "ps", "eps", and "svg".
     pil_kwargs : dict, optional
         Keyword arguments passed to `PIL.Image.Image.save`.  If the 'pnginfo'
         key is present, it completely overrides *metadata*, including the
@@ -1674,6 +1675,8 @@ def imsave(fname, arr, vmin=None, vmax=None, cmap=None, format=None,
                 for k, v in metadata.items():
                     if v is not None:
                         pnginfo.add_text(k, v)
+        elif metadata is not None:
+            raise ValueError(f"metadata not supported for format {format!r}")
         if format in ["jpg", "jpeg"]:
             format = "jpeg"  # Pillow doesn't recognize "jpg".
             facecolor = mpl.rcParams["savefig.facecolor"]
diff --git a/lib/matplotlib/tests/test_figure.py b/lib/matplotlib/tests/test_figure.py
index 80d80f969163..f51ce72937a2 100644
--- a/lib/matplotlib/tests/test_figure.py
+++ b/lib/matplotlib/tests/test_figure.py
@@ -1548,3 +1548,14 @@ def test_gridspec_no_mutate_input():
     plt.subplots(1, 2, width_ratios=[1, 2], gridspec_kw=gs)
     assert gs == gs_orig
     plt.subplot_mosaic('AB', width_ratios=[1, 2], gridspec_kw=gs)
+
+
+@pytest.mark.parametrize('fmt', ['eps', 'pdf', 'png', 'ps', 'svg', 'svgz'])
+def test_savefig_metadata(fmt):
+    Figure().savefig(io.BytesIO(), format=fmt, metadata={})
+
+
+@pytest.mark.parametrize('fmt', ['jpeg', 'jpg', 'tif', 'tiff', 'webp', "raw", "rgba"])
+def test_savefig_metadata_error(fmt):
+    with pytest.raises(ValueError, match="metadata not supported"):
+        Figure().savefig(io.BytesIO(), format=fmt, metadata={})