diff --git a/src/fromager/pkgmetadata/pep639.py b/src/fromager/pkgmetadata/pep639.py
index 53fc24a6..d0119209 100644
--- a/src/fromager/pkgmetadata/pep639.py
+++ b/src/fromager/pkgmetadata/pep639.py
@@ -81,6 +81,8 @@ def _trove_to_spdx(troves: list[str]) -> LicenseExpression:
         if mapped is None:
             raise ValueError(f"{trove!r} is ambiguous")
         trove_spdx.append(mapped)
+    if not trove_spdx:
+        raise ValueError("no classifier maps to a SPDX license expression")
     # join with AND
     return _parse_spdx(" AND ".join(trove_spdx), simplify=True)
 
diff --git a/tests/test_pkgmetadata.py b/tests/test_pkgmetadata.py
index 0eb8baac..1bb40850 100644
--- a/tests/test_pkgmetadata.py
+++ b/tests/test_pkgmetadata.py
@@ -108,6 +108,18 @@ def test_license_from_metadata(metadata: Metadata, expected: str) -> None:
         (None, None, None),
         (None, "invalid", None),
         (None, None, ["License :: OSI Approved :: BSD License"]),
+        # classifiers with no entry that maps to SPDX (see issue #1372)
+        (None, None, ["Programming Language :: Python :: 3"]),
+        (None, None, ["License :: OSI Approved"]),
+        # non-license classifier alongside an ambiguous license classifier
+        (
+            None,
+            None,
+            [
+                "Programming Language :: Python :: 3",
+                "License :: OSI Approved :: BSD License",
+            ],
+        ),
     ],
 )
 def test_license_from_metadata_errors(