In this paper we propose strategies to alleviate the impact of noise on data-driven model-order reduction by moment matching. We classify the noise affecting the data-driven methods as interconnection noise and measurement noise. We then consider two statistical models of the noise, namely Gaussian (white noise) and Student’s t, to represent noise in a variety of applications. We propose and study the use of Wavelet denoising for dealing with white noise and the use of Huber regression for the Student’s t-distribution. We demonstrate by means of extensive simulations how these strategies improve the accuracy and robustness of the data-driven algorithms.