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We demonstrate the creation of an electromagnetic bandgap (stopband) within the passband of the fundamental mode of a substrate-integrated waveguide. The bandgap is achieved by periodically modulating the waveguide width using the metallic plated vias that form the effective waveguide sidewall. We describe the design of such a structure, noting that, compared with previously demonstrated 1-D transmission-line electromagnetic bandgap structures, the resonant bandgap frequency is more significantly affected by the amplitude (depth) of the modulation of the waveguide width. We explain this result using classical circuit theory and describe a model-based approach to predicting device behavior. We present measured results for several designed structures in the Ka-band using smooth and square-like modulations of the waveguide width. We demonstrate both uniform and linearly chirped (dispersive) implementations; the latter structures yield broadband linear group delays in the reflected band.