  We model Raman processes in silicene and germanene involving scattering of
quasiparticles by, either, two phonons, or, one phonon and one point defect. We
compute the resonance Raman intensities and lifetimes for laser excitations
between 1 and 3$\,$eV using a newly developed third-nearest neighbour
tight-binding model parametrized from first principles density functional
theory. We identify features in the Raman spectra that are unique to the
studied materials or the defects therein. We find that in silicene, a new Raman
resonance arises from the $2.77\,\rm$eV $\pi-\sigma$ plasmon at the M point,
measurably higher than the Raman resonance originating from the $2.12\,\rm$eV
$\pi$ plasmon energy. We show that in germanene, the lifetimes of charge
carriers, and thereby the linewidths of the Raman peaks, are influenced by
spin-orbit splittings within the electronic structure. We use our model to
predict scattering cross sections for defect induced Raman scattering involving
adatoms, substitutional impurities, Stone-Wales pairs, and vacancies, and argue
that the presence of each of these defects in silicene and germanene can be
qualitatively matched to specific features in the Raman response.
