diff --git a/Lib/email/Message.py b/Lib/email/Message.py
index 512a0e91dc3..00efbcc0cf4 100644
--- a/Lib/email/Message.py
+++ b/Lib/email/Message.py
@@ -227,12 +227,16 @@ class Message:
         These will be sorted in the order they appeared in the original
         message, and may contain duplicates.  Any fields deleted and
         re-inserted are alwyas appended to the header list.
+
+        If no such fields exist, failobj is returned (defaults to None).
         """
         values = []
         name = name.lower()
         for k, v in self._headers:
             if k.lower() == name:
                 values.append(v)
+        if not values:
+            return failobj
         return values
 
     def add_header(self, _name, _value, **_params):