A novel class of substrate-integrated waveguides (SIWs) is presented, based on the concept of the classical ridge rectangular waveguide, which permits the design of broadband, compact and low-loss integrated components and interconnects. Two configurations are proposed. The former is the ridge SIW, where the structure is integrated in a dielectric substrate with top and bottom metal layers, and comprises two-sided rows of full-height metal cylinders and a central row of partial-height metal posts connected at their bottom by a metal strip. The latter is the ridge substrate-integrated slab waveguide; this structure presents a geometry similar to the ridge SIW, but includes additional air holes to further enhance the bandwidth. The design and experimental verification of two prototypes, covering the frequency band from 6.8 to 25 GHz and from 7.1 to 30.7 GHz, respectively, are also presented. The proposed structures exhibit a mono-modal bandwidth three times broader than classical rectangular waveguides or SIWs, and their size is half of the SIW with the same cut-off frequency.