Abstract. It has been proposed that microscopic black holes can catalyze decay of metastable false vacuum. Previous calculations made use of the Euclidean time formalism developed for equilibrium configurations. This is not the case, however, for a realistic black hole formed by gravitational collapse and emitting Hawking radiation. I will review the motivations to study black hole catalysis of vacuum decay, propose a semiclassical method to calculate the decay rate, and illustrate it on an example of a two-dimensional toy model, with emphasis on the role played by the black hole greybody factors. The proposed formalism is not limited to black holes and applies to tunneling in out-of-equilibrium systems in general.