In this paper, we investigate the performance of regularized MP2-like methods for some prototypical periodic systems, which each constitute known issues for canonical MP2. In particular, we consider the homogeneous electron gas (a metal prototype), the one-dimensional Hubbard model (a strongly correlated system) and the interaction of graphene with a water molecule (a challenging dispersion-driven interaction). We also propose a new, non-empirical regularization method based on second-order Brillouin-Wigner perturbation theory.