In this article, we develop methods for estimating the expected time to the first loss in an Erlang loss system. We are primarily interested in estimating this quantity under light traffic conditions. We propose and compare three simulation techniques as well as two Markov chain approximations. We show that the Markov chain approximations proposed by us are asymptotically exact when the load offered to the system goes to zero. The article also serves to highlight the fact that efficient estimation of transient quantities of stochastic systems often requires the use of techniques that combine analytical results with simulation.