Panel data have been increasingly used over the past decades. They arise in various fields of study like economics, biology, marketing, finance, the environment, and others. Particularly in domains of economics and finance, panel (or longitudinal) data are frequently used. Usually, research is based on empirical studies, where the estimation of the parameters is usually obtained with classical methodologies. Real data frequently exhibit the presence of outliers. These values may have a serious effect on the classic estimates produced. This paper aims to provide robust methods of estimation for random effects in panel data, resulting in better estimates for the parameters when the data violate the assumed conditions of the classic estimation models. The properties of the proposed estimation methods are measured with Monte Carlo simulations. A real data set is used to illustrate the new suggested methodology performance.