We show how to apply Howe's method for the proof of congruence of early bisimilarities in a higher-order process calculus with passivation. This involves the introduction of a proof technique based on a new kind of transition system and bisimilarity, 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. We apply this technique to obtain the first characterization of weak barbed congruence for such a higher-order calculus with passivation.