We present a computational study of the two-phonon Raman spectra of silicene and graphene within a density-functional non-orthogonal tight-binding model. Due to the presence of linear bands close to the Fermi energy in the electronic structure of both structures, the Raman scattering by phonons is resonant. We find that the Raman spectra exhibit a crossover behavior for laser excitation close to the π -plasmon energy. This phenomenon is explained by the disappearance of certain paths for resonant Raman scattering and the appearance of other paths beyond this energy. Besides that, the electronic joint density of states (DOS) is divergent at this energy, which is reflected on the behavior of the Raman bands of the two structures in a qualitatively different way. Additionally, a number of Raman bands, originating from divergent phonon DOS at the M point and at points, inside the Brillouin zone, is also predicted. The calculated spectra for graphene are in excellent agreement with available experimental data. The obtained Raman bands can be used for structural characterization of silicene and graphene samples by Raman spectroscopy.