Matchers.any(Class) will do the trick:
Mockito.when(object.doThings(Matchers.any(MyEnum.class), Matchers.anyLong()))
.thenReturn(123L);
null will be excluded with Matchers.any(Class). If you want to include null you must use the more generic Matchers.any().
As a side note: consider using Mockito static imports:
import static org.mockito.Matchers.*;
import static org.mockito.Mockito.*;
Mocking gets a lot shorter:
when(object.doThings(any(MyEnum.class), anyLong())).thenReturn(123L);