A technique is discussed for calculating the electromagnetic field in two-dimensional inductive plasmas with an arbitrary number of magnetic materials and load coils. The method is a generalization of the boundary-relaxation technique for systems with an arbitrary number of conducting regions, and extends its applicability to systems which contain magnetically active materials. Each material is defined on a distinct ortho-curvilinear numerical structured mesh. This facilitates the coupling of the electromagnetic model with the calculation of material transport, in which typically only one of these grids is involved. The method allows an exact and straightforward formulation of the boundary conditions and has the additional advantage that only current-carrying regions of space need to be discretized. The technique has been verified by running the model for a number of test cases for which analytical solutions exist, and later applied to a geometry which is characteristic for plasma induction lamps. A selection of these results will be demonstrated and discussed.