We have explored a new strategy to discover materials with large resistive or capacitive responses to magnetic fields by synthesizing EuMO2N (M = Nb, Ta) perovskites that combine ferromagnetic order of S = 7/2 Eu2+ spins with possible offcenter distortions of the d(0) M5+ cations enhanced by covalent bonding to N. EuNbO2N shows colossal magnetoresistances at low temperatures and a giant magnetocapacitance. However, the latter response originates from a microstructural effect rather than an intrinsic multiferroism.