We consider a Gaussian process model trained on few evaluations of an expensive-to-evaluate deterministic function and we study the problem of estimating a fixed excursion set of this function. We review the concept of conservative estimates, recently introduced in this framework, and, in particular, we focus on estimates based on Vorob'ev quantiles. We present a method that sequentially selects new evaluations of the function in order to reduce the uncertainty on such estimates. The sequential strategies are first benchmarked on artificial test cases generated from Gaussian process realizations in two and five dimensions, and then applied to two reliability engineering test cases.