The multiple objective sequential optimization (MOSO) is one of the recent fronteers of the multiple objectives optimization strategies. Such an optimization is applied, for the first time in the open literature, to the optimization of the performances of a common mode filter based on a planar electromagnetic (EM) bandgap structure. The relevant design variables of this component are evaluated to increase the ${\rm{S}}_{{\rm{cc21}}}$ bandwidth around the design frequency and to decrease the unwanted total EM radiated power. The MOSO implements, for the optimization, a differential evolutionary (DE) algorithm. The results are validated either by measurement or by the computations obtained by substituting the DE with a standard genetic algorithm.