In this paper an approach is proposed which is based on a method of regularization for estimating the solution of inverse problems of electromagnetic with noisy measurements. The constraints on the solution of the inverse problem based on physical assumptions are taken into consideration. The solution is reduced to a nonlinear system with the given interval-type inaccuracy of the right-hand side. The developed approach enables one to take into account inaccuracy of the operator of the inverse problem. The method of the special mathematical model selection is described which improves the accuracy of estimations.