The Huber function is known to yield robust estimations reducing the effect of outliers. We introduced previously a regularization approach for quantitative microwave imaging based on the Huber function, which is suitable not only for piece-wise constant, but also for more general permittivity profiles (that are of interest e.g. in biomedical imaging). We demonstrated already very encouraging first results on simulated data. In this paper, we perform thorough analysis of this regularizer, studying the influence of the parameters under different noise levels. Moreover, we evaluate the whole approach not only on simulated data but also on real 3D electromagnetic measurements. Our focus is on reconstructions from relatively few measurements (sparse measurements) to speed up the reconstruction process. The results on experimental data from the 3D Fresnel database motivate strongly the use of Huber regularization. The advantages over related regularization methods, that were demonstrated previously on simulated data are now confirmed with real experimental data. Moreover, thorough analysis of the influence of different parameters presented in this paper gives new insights in the behavior of the Huber regularizer in quantitative microwave imaging and provides useful guidelines for its practical use in different scenarios (e.g. different levels of measurement noise).