Copula functions are very convenient for modelling multivariate observations. Popular estimation methods are the two-stage MLE and an alternative semi-parametric with empirical cdf for the margins. Unfortunately, they are hastily biased whenever relatively small model deviations occur at the marginal (empirical or parametric) and/or copula levels. In this master thesis we propose three robust estimators that do not share this undesirable feature. The bounded-bias of robust estimators is corrected through indirect inference. By means of a simulation study we show that the robust estimators outperform the popular approaches.