Coupling between non-adjacent resonators and wave propagation through the waveguide structure in distributed EM filters are reduced by forming one or more holes in one or more of the resonators (planar or folded) and by passing a conductive structure through each hole normal to the resonator. The conductive structures (vertical vias or horizontal strips) are preferably grounded, either by direct connection or capacitive coupling to one or more ground planes or by creation of a virtual ground. The holes are spaced apart from the edges of the resonator so as to minimize any interference with the current and fields concentrated at the edges of each resonator. These conductive structures narrow the effective cavity width “aeff” for the waveguide as a whole and between non-adjacent resonators without affecting the cavity width “a” between adjacent resonators. Consequently the conductive structures have no effect on the desired coupling between adjacent resonators and the desired filter response of parallel-coupled filters while increasing the attenuation of the wave propagating in the waveguide and the attenuation of the wave coupled between non-adjacent resonators.