A parallel plate waveguide structure may be configured to suppress spurious propagating modes by including a lossy frequency selective surface (FSS) formed from a resistive film. The electromagnetic material properties of individual layers disposed between the conductive plates of the waveguide may be engineered to extend the suppression band of the fundamental TE mode up to the cutoff frequency of the second TE mode, and to simultaneously create a multi-octave TM mode suppression band. Applications include, for example, cavity mode suppression in microwave and millimeterwave assemblies at the board, package, and chip level.