diff --git a/pygit2/branches.py b/pygit2/branches.py
index 77cabfc1..5819333f 100644
--- a/pygit2/branches.py
+++ b/pygit2/branches.py
@@ -28,7 +28,7 @@
 from collections.abc import Iterator
 from typing import TYPE_CHECKING
 
-from ._pygit2 import Branch, Commit, Oid
+from ._pygit2 import Branch, Commit, InvalidSpecError, Oid
 from .enums import BranchType, ReferenceType
 
 # Need BaseRepository for type hints, but don't let it cause a circular dependency
@@ -72,11 +72,13 @@ def __getitem__(self, name: str) -> Branch:
 
         return branch
 
-    def get(self, key: str) -> Branch:
+    def get(self, key: str) -> Branch | None:
         try:
             return self[key]
-        except KeyError:
-            return None  # type:ignore #  next commit
+        except (KeyError, InvalidSpecError):
+            # As in References.get: git_branch_lookup reports
+            # GIT_EINVALIDSPEC for a name that is not a valid branch name.
+            return None
 
     def __iter__(self) -> Iterator[str]:
         for branch_name in self._repository.listall_branches(self._flag):
diff --git a/pygit2/references.py b/pygit2/references.py
index 533e90ab..4094bb56 100644
--- a/pygit2/references.py
+++ b/pygit2/references.py
@@ -30,6 +30,7 @@
 
 from pygit2 import Oid
 
+from ._pygit2 import InvalidSpecError
 from .enums import ReferenceFilter
 
 # Need BaseRepository for type hints, but don't let it cause a circular dependency
@@ -48,7 +49,10 @@ def __getitem__(self, name: str) -> 'Reference':
     def get(self, key: str) -> 'Reference' | None:
         try:
             return self[key]
-        except KeyError:
+        except (KeyError, InvalidSpecError):
+            # git_reference_lookup reports GIT_EINVALIDSPEC as well as
+            # GIT_ENOTFOUND for a name it cannot resolve; only the latter
+            # arrives as a KeyError.
             return None
 
     def __iter__(self) -> Iterator[str]:
diff --git a/test/test_branch.py b/test/test_branch.py
index 14cb965f..e6f5940c 100644
--- a/test/test_branch.py
+++ b/test/test_branch.py
@@ -85,11 +85,13 @@ def test_branches_delete_error(testrepo: Repository) -> None:
 
 def test_branches_is_head(testrepo: Repository) -> None:
     branch = testrepo.branches.get('master')
+    assert branch is not None
     assert branch.is_head()
 
 
 def test_branches_is_not_head(testrepo: Repository) -> None:
     branch = testrepo.branches.get('i18n')
+    assert branch is not None
     assert not branch.is_head()
 
 
@@ -98,34 +100,40 @@ def test_branches_rename(testrepo: Repository) -> None:
     assert new_branch.target == I18N_LAST_COMMIT
 
     new_branch_2 = testrepo.branches.get('new-branch')
+    assert new_branch_2 is not None
     assert new_branch_2.target == I18N_LAST_COMMIT
 
 
 def test_branches_rename_error(testrepo: Repository) -> None:
     original_branch = testrepo.branches.get('i18n')
+    assert original_branch is not None
     with pytest.raises(ValueError):
         original_branch.rename('master')
 
 
 def test_branches_rename_force(testrepo: Repository) -> None:
     original_branch = testrepo.branches.get('master')
+    assert original_branch is not None
     new_branch = original_branch.rename('i18n', True)
     assert new_branch.target == LAST_COMMIT
 
 
 def test_branches_rename_invalid(testrepo: Repository) -> None:
     original_branch = testrepo.branches.get('i18n')
+    assert original_branch is not None
     with pytest.raises(ValueError):
         original_branch.rename('abc@{123')
 
 
 def test_branches_name(testrepo: Repository) -> None:
     branch = testrepo.branches.get('master')
+    assert branch is not None
     assert branch.branch_name == 'master'
     assert branch.name == 'refs/heads/master'
     assert branch.raw_branch_name == branch.branch_name.encode('utf-8')
 
     branch = testrepo.branches.get('i18n')
+    assert branch is not None
     assert branch.branch_name == 'i18n'
     assert branch.name == 'refs/heads/i18n'
     assert branch.raw_branch_name == branch.branch_name.encode('utf-8')
@@ -268,3 +276,16 @@ def test_branch_name(testrepo: Repository) -> None:
     branch = testrepo.lookup_branch('i18n')
     assert branch.branch_name == 'i18n'
     assert branch.name == 'refs/heads/i18n'
+
+
+def test_branches_get_invalid_name(testrepo: Repository) -> None:
+    """Branches.get() returns None for a name that is not a valid branch name.
+
+    git_branch_lookup reports GIT_EINVALIDSPEC for these, which arrives as
+    InvalidSpecError rather than KeyError.
+    """
+    repo = testrepo
+
+    assert repo.branches.get('my branch') is None
+    assert 'my branch' not in repo.branches
+    assert repo.branches.get('does-not-exist') is None
diff --git a/test/test_branch_empty.py b/test/test_branch_empty.py
index b0ef793c..7934c60b 100644
--- a/test/test_branch_empty.py
+++ b/test/test_branch_empty.py
@@ -42,6 +42,7 @@ def repo(emptyrepo: Repository) -> Generator[Repository, None, None]:
 
 def test_branches_remote_get(repo: Repository) -> None:
     branch = repo.branches.remote.get('origin/master')
+    assert branch is not None
     assert branch.target == ORIGIN_MASTER_COMMIT
     assert repo.branches.remote.get('origin/not-exists') is None
 
diff --git a/test/test_packbuilder.py b/test/test_packbuilder.py
index 06410699..c3552c0c 100644
--- a/test/test_packbuilder.py
+++ b/test/test_packbuilder.py
@@ -75,6 +75,7 @@ def test_pack_with_delegate(testrepo: Repository, tmp_path: Path) -> None:
     def pack_delegate(pb: PackBuilder) -> None:
         for branch in pb._repo.branches:
             br = pb._repo.branches.get(branch)
+            assert br is not None
             for commit in br.log():
                 pb.add_recur(commit.oid_new)
 
diff --git a/test/test_refs.py b/test/test_refs.py
index 80c59fc9..f2e35fdb 100644
--- a/test/test_refs.py
+++ b/test/test_refs.py
@@ -466,6 +466,26 @@ def test_lookup_reference(testrepo: Repository) -> None:
     assert reference.name == 'refs/heads/master'
 
 
+def test_references_get_invalid_name(testrepo: Repository) -> None:
+    """A name libgit2 rejects as a spec is still "not found" to get().
+
+    git_reference_lookup reports GIT_EINVALIDSPEC as well as GIT_ENOTFOUND,
+    and only the latter reaches pygit2 as a KeyError.
+    """
+    repo = testrepo
+
+    # 'master' is not a full reference name, so libgit2 calls it invalid.
+    assert repo.references.get('master') is None
+    assert 'master' not in repo.references
+
+    # A well-formed name that does not exist behaves the same way.
+    assert repo.references.get('refs/heads/does-not-exist') is None
+
+    # __getitem__ still raises, as documented.
+    with pytest.raises((KeyError, InvalidSpecError)):
+        repo.references['master']
+
+
 def test_lookup_reference_dwim(testrepo: Repository) -> None:
     repo = testrepo