diff --git a/src/cpyrt/Utility.cxx b/src/cpyrt/Utility.cxx
index 9e947e9..0761fc5 100644
--- a/src/cpyrt/Utility.cxx
+++ b/src/cpyrt/Utility.cxx
@@ -659,7 +659,7 @@ std::string cpyrt::Utility::ConstructTemplateArgs(PyObject* pyname,
                        (args ? PyTuple_GET_ITEM(args, i) : nullptr), pref,
                        pcnt)) {
         PyErr_SetString(
-            PyExc_SyntaxError,
+            PyExc_TypeError,
             "could not construct C++ name from provided template argument.");
         return "";
       }
@@ -827,6 +827,12 @@ static bool AddTypeName(std::vector<Cpp::TemplateArgInfo>& types, PyObject* tn,
     if (tpName) {
       interop::TCppType_t type = interop::GetType(
           cpyrt_PyText_AsString(tpName), /* enable_slow_lookup */ true);
+      if (!type) {
+        // any Python object has a __name__; one that does not name a C++
+        // type contributes no argument
+        Py_DECREF(tpName);
+        continue;
+      }
       if (interop::IsEnumType(type)) {
         PyObject* value_int = PyNumber_Index(tn);
         if (!value_int) {
diff --git a/test/test_regression.py b/test/test_regression.py
index af96a3b..945e4d3 100644
--- a/test/test_regression.py
+++ b/test/test_regression.py
@@ -1631,3 +1631,15 @@ def test51_nontype_enum_template_arg(self):
 
         # ...nor leave the interpreter unable to compile a later call wrapper
         assert ns.probe(41) == 42
+
+    def test52_no_cpp_name_for_template_arg(self):
+        """Template arguments with no C++ equivalent raise TypeError"""
+
+        import cppjit
+
+        # a lambda has a __name__ ("<lambda>") that resolves to no C++ type
+        with raises(TypeError):
+            cppjit.gbl.std.vector[lambda: None]
+
+        with raises(TypeError):
+            cppjit.gbl.std.vector[object()]