This report shows how to apply Howe's method for the proof of congruence of early bisimilarities in higher-order process calculi. This involves the introduction of a new kind of transition system and a new kind of bisimilarity, collectively called complementary semantics. We show that complementary semantics is equivalent to contextual semantics, originally introduced by Sangiorgi, that relies on classical transition systems for higher-order calculi and context bisimilarity.