The ability of gratings made of dielectric ridges placed on top of flat metal layers to open gaps in the dispersion relation of surface plasmon polaritons (SPPs) is studied, both experimentally and theoretically. The gap position can be approximately predicted by the same relation as for standard optical Bragg stacks. The properties of the gap as a function of the grating parameters is numerically analyzed by using the Fourier modal method, and the presence of the gap is experimentally confirmed by leakage radiation microscopy. We also explore the performance of these dielectric gratings as SPP Bragg mirrors. The results show very good reflecting properties of these mirrors for a propagating SPP whose wavelength is inside the gap.