Hidden Markov Models (HMMs) is a powerful tool to model phenomena with complex time dependencies, where each observation is assumed to depend on the current state of a dynamical system, itself unobserved (hidden/latent variable). There are numerous methods (least squares, maximum likelihood, spectral estimator, ...) and results for the estimation of the parameters of HMMs (Markov kernel, initial distribution, emission distributions, order) when they are identifiable. Recent works of Lehéricy filled a gap in the literature with nonparametric and nonasymptotic bounds for the common estimation of the different parameters. Still, there is no general result of robust estimation in the context of HMMs.  We propose a procedure for estimating the parameters of HMMs that is optimal or nearly optimal when the model is exact and whose performance remains stable when the model is slightly misspecified. In particular, we show that a sufficiently small amount of outliers or contaminating data among the observations has little influence on the performance  of our estimator.