© 2018 American Physical Society. We recently proposed a high-pressure and high-temperature P62m-symmetry polymorph for CaF2 on the basis of ab initio random structure searching and density-functional theory calculations [J. R. Nelson et al., Phys. Rev. B 95, 054118 (2017)2469-995010.1103/PhysRevB.95.054118]. We revisit this polymorph using both ab initio and classical molecular dynamics simulations. The structure undergoes a phase transition to a superionic phase in which calcium ions lie on a bcc-symmetry lattice (space group Im3m), a phase not previously discussed for the group-II difluorides. We demonstrate that modeling this phase transition is surprisingly difficult and requires very large simulation cells (at least 864 atoms) in order to observe correct qualitative and quantitative behavior. The prediction of superionic behavior in P62m CaF2 was originally made through the observation of a lattice instability at the harmonic level in DFT calculations. Using superionic α-CaF2, CeO2, β-PbF2, and Li2O as examples, we examine the potential of using phonons as a means to search for superionic materials and propose that this offers an affordable way to do so.