diff --git a/src/curies/api.py b/src/curies/api.py
index 684433f..4970757 100644
--- a/src/curies/api.py
+++ b/src/curies/api.py
@@ -210,6 +210,18 @@ def __str__(self) -> str:  # noqa:D105
         return f"Duplicate prefixes:\n{self._str()}"
 
 
+class ConversionError(ValueError):
+    """An error raised on conversion."""
+
+
+class ExpansionError(ConversionError):
+    """An error raised on expansion if the prefix can't be looked up."""
+
+
+class CompressionError(ConversionError):
+    """An error raised on expansion if the URI prefix can't be matched."""
+
+
 def _get_duplicate_uri_prefixes(records: List[Record]) -> List[Tuple[Record, Record, str]]:
     return [
         (record_1, record_2, uri_prefix)
@@ -684,6 +696,13 @@ def format_curie(self, prefix: str, identifier: str) -> str:
         """Format a prefix and identifier into a CURIE string."""
         return f"{prefix}{self.delimiter}{identifier}"
 
+    def compress_strict(self, uri: str) -> str:
+        """Compress a URI to a CURIE, and raise an error of not possible."""
+        rv = self.compress(uri)
+        if rv is None:
+            raise CompressionError(uri)
+        return rv
+
     def compress(self, uri: str) -> Optional[str]:
         """Compress a URI to a CURIE, if possible.
 
@@ -733,6 +752,13 @@ def parse_uri(self, uri: str) -> Union[ReferenceTuple, Tuple[None, None]]:
         else:
             return ReferenceTuple(prefix, uri[len(value) :])
 
+    def expand_strict(self, curie: str) -> str:
+        """Expand a CURIE to a URI, and raise an error of not possible."""
+        rv = self.expand(curie)
+        if rv is None:
+            raise ExpansionError(curie)
+        return rv
+
     def expand(self, curie: str) -> Optional[str]:
         """Expand a CURIE to a URI, if possible.
 
diff --git a/tests/test_api.py b/tests/test_api.py
index 92a449c..9ad8e2c 100644
--- a/tests/test_api.py
+++ b/tests/test_api.py
@@ -13,9 +13,11 @@
 from bioregistry.export.prefix_maps import EXTENDED_PREFIX_MAP_PATH
 
 from curies.api import (
+    CompressionError,
     Converter,
     DuplicatePrefixes,
     DuplicateURIPrefixes,
+    ExpansionError,
     Record,
     Reference,
     ReferenceTuple,
@@ -113,10 +115,17 @@ def _assert_convert(self, converter: Converter):
             ("OBO:unnamespaced", "http://purl.obolibrary.org/obo/unnamespaced"),
         ]:
             self.assertEqual(curie, converter.compress(uri))
+            self.assertEqual(curie, converter.compress_strict(uri))
             self.assertEqual(uri, converter.expand(curie))
+            self.assertEqual(uri, converter.expand_strict(curie))
 
         self.assertIsNone(converter.compress("http://example.org/missing:00000"))
+        with self.assertRaises(CompressionError):
+            converter.compress_strict("http://example.org/missing:00000")
+
         self.assertIsNone(converter.expand("missing:00000"))
+        with self.assertRaises(ExpansionError):
+            converter.expand_strict("missing:00000")
 
         self.assertLess(0, len(converter.records), msg="converter has no records")
         self.assertIsNone(converter.get_record("nope"))