The Proper Orthogonal Decomposition (POD) is an interesting approach to compress into a reduced basis numerous solutions obtained from a parametrized Finite Element (FE) model. In order to obtain a fast approximation of a FE solution, the POD can be combined with an interpolation method based on Radial Basis Functions (RBF) to interpolate the coordinates of the solution into the reduced basis. In this paper, this POD-RBF approach is applied to a nonlinear magnetostatic problem and is used with a single phase transformer and a three-phase inductance.