Behavioral theory for higher-order process calculi is less well devel- oped than for first-order ones such as the π-calculus. The most natural process equivalence relation, barbed congruence, is difficult to use in practice because of the infinite number of test contexts it requires. One is therefore lead to find simpler characterizations of barbed congruence, which may not be easy to do for higher-order process calculi, especially in the weak case. Such characterizations have been obtained for some calculi. For instance, in the case of the higher π-calculus, HOπ, Sangiorgi has defined a notion of normal bisimulation, which characterizes barbed congruence and that requires only a finite number of tests. In this paper, we study bisimulations in higher-order calculi with a passivation operator, that allows the interruption and thunkification of a running process. We develop a normal bisimulation that characterizes barbed congruence, in the strong and weak cases, in a higher-order calculus with passivation, but without name restriction. We then show that this characterization result does not hold in the presence of name restriction.