We consider intermittency in one-parameter families of unimodal maps, induced by saddle node and boundary crisis bifurcations. In these bifurcations either a periodic orbit or a periodic interval disappears to give rise to chaotic bursts. We prove asymptotic formulae for the frequency with which orbits visit the region previously occupied by the attractor. For this, we extend Pianigiani's results on conditionally invariant measures for the logistic family to more general families.