diff --git a/pygmt/helpers/decorators.py b/pygmt/helpers/decorators.py
index e6b87180cd1..eb3383f328d 100644
--- a/pygmt/helpers/decorators.py
+++ b/pygmt/helpers/decorators.py
@@ -567,16 +567,13 @@ def new_module(*args, **kwargs):
                     )
                     warnings.warn(msg, category=SyntaxWarning, stacklevel=2)
 
-            # timestamp (U) is deprecated since v0.9.0.
+            # timestamp (U) is deprecated since v0.9.0 and removed in v0.12.0.
             if "U" in kwargs or "timestamp" in kwargs:
-                if "timestamp" in kwargs:
-                    kwargs["U"] = kwargs.pop("timestamp")
                 msg = (
-                    "Parameters 'U' and 'timestamp' are deprecated since v0.9.0 "
-                    "and will be removed in v0.12.0. "
+                    "Parameters 'U' and 'timestamp' are no longer supported since v0.12.0. "
                     "Use Figure.timestamp() instead."
                 )
-                warnings.warn(msg, category=SyntaxWarning, stacklevel=2)
+                raise GMTInvalidInput(msg)
 
             # xshift (X) is deprecated since v0.8.0.
             if "X" in kwargs or "xshift" in kwargs:
diff --git a/pygmt/tests/test_timestamp.py b/pygmt/tests/test_timestamp.py
index 3a5e9506574..0d7f42493c2 100644
--- a/pygmt/tests/test_timestamp.py
+++ b/pygmt/tests/test_timestamp.py
@@ -2,7 +2,8 @@
 Test Figure.timestamp.
 """
 import pytest
-from pygmt import Figure, config
+from pygmt import Figure
+from pygmt.exceptions import GMTInvalidInput
 
 
 @pytest.fixture(scope="module", name="faketime")
@@ -95,36 +96,16 @@ def test_timestamp_text_truncated():
     return fig
 
 
-@pytest.mark.mpl_image_compare(filename="test_timestamp.png")
-def test_timestamp_deprecated_timestamp(faketime):
-    """
-    Check if the deprecated parameter 'timestamp' works but raises a warning.
+def test_timestamp_unsupported_u_timestamp():
     """
-    fig = Figure()
-    with pytest.warns(expected_warning=SyntaxWarning) as record:
-        with config(FORMAT_TIME_STAMP=faketime):
-            # plot nothing (the data is outside the region) but a timestamp
-            fig.plot(
-                x=0,
-                y=0,
-                style="p",
-                projection="X1c",
-                region=[1, 2, 1, 2],
-                timestamp=True,
-            )
-        assert len(record) == 1  # check that only one warning was raised
-    return fig
+    Raise an exception when either U or timestamp is used.
 
-
-@pytest.mark.mpl_image_compare(filename="test_timestamp.png")
-def test_timestamp_deprecated_u(faketime):
-    """
-    Check if the deprecated parameter 'U' works but raises a warning.
+    Parameters U and timestamp are no longer supported since v0.12.0.
     """
     fig = Figure()
-    with pytest.warns(expected_warning=SyntaxWarning) as record:
-        with config(FORMAT_TIME_STAMP=faketime):
-            # plot nothing (the data is outside the region) but a timestamp
-            fig.plot(x=0, y=0, style="p", projection="X1c", region=[1, 2, 1, 2], U=True)
-        assert len(record) == 1  # check that only one warning was raised
-    return fig
+    with pytest.raises(GMTInvalidInput):
+        fig.plot(x=0, y=0, style="p", projection="X1c", region=[1, 2, 1, 2], U=True)
+    with pytest.raises(GMTInvalidInput):
+        fig.plot(
+            x=0, y=0, style="p", projection="X1c", region=[1, 2, 1, 2], timestamp=True
+        )