Statistical model checking has become a promising technique to circumvent the state space explosion problem in model-based verification. It trades time for memory, via a probabilistic simulation and exploration of the model behaviour—often combined with effective a posteriori hypothesis testing. However, as a simulation-based approach, it can only provide sound verification results if the underlying model is a stochastic process. This drastically limits its applicability in verification, where most models are indeed variations of nondeterministic transition systems. In this paper, we describe a sound extension of statistical model checking to scenarios where nondeterminism is present. We focus on probabilistic automata, and discuss how partial order reduction can be twisted such as to apply statistical model checking to models with spurious nondeterminism. We report on an implementation of this technique and on promising results in the context of verification and dependability analysis of distributed systems.