A transmission line format is presented which takes the form of a Multilayer Ridged Substrate Integrated Waveguide, for which signal energy is transmitted within standard PCB substrates, within a wave-guiding structure formed from conducting tracks in the horizontal plane and arrays of through-plated vias in the vertical plane.The Substrate Integrated Waveguide (SIW) is a recent development into which research is so far concentrated on single-layer rectangular variants which, like traditional rectangular waveguide, are amenable to analytic computation of the cutoff eigenvalues. Recent publications have offered empirically-derived relationships with which a Substrate Integrated Waveguide can be analysed by equivalence of the horizontal dimensions with a conventional waveguide, allowing such structures to be designed with minimal effort.We propose a ridged form of this structure, in which multiple PCB layers are stacked to obtain the desired height and the published equivalent width is used to obtain the horizontal dimensions. The proposed structure combines the increased bandwidth of ridged waveguide with SIW's greatly reduced cost of manufacture and integration, relative to conventional waveguide, and improved power handling capacity and loss susceptibility relative to microstrip.Ridged variants have not yet been studied in the literature, however, in part because the eigenspectrum can not be obtained analytically. We thus present a semi-analytical software model with which to synthesise and analyse the cutoff spectrum in ridged Substrate Integrated Waveguide, verified by comparison with analytical solutions, where they exist, simulation in finite-element software and a physical prototype. Agreement with simulated and measured results is within 1 % in certain subsets of the parameter space and 11 % generally, and individual results are returned in times of the order of seconds.We use the model to analyse the relationship between geometry and frequency response, constructing an approximating function for the early modes which is significantly faster, such that think it can be used for first-pass optimisation. A range of optimal parameters are presented which maximise bandwidth within anticipated planar geometric constraints, and typical design scenarios are explored.