The effects of the finite size of the simulation box in equilibrium molecular dynamics simulations are investigated for prototypical superionic conductors of different types, namely, the fluorite-structure materials PbF2, CaF2, and UO2 (type II), and the alpha phase of AgI (type I). Largely validated empirical force-fields are employed to run ns-long simulations and extract general trends for several properties, at increasing size and in a wide temperature range. This work shows that, for the considered type-II superionic conductors, the diffusivity dramatically depends on the system size and that the superionic regime is shifted to larger temperatures in smaller cells. Furthermore, only simulations of several hundred atoms are able to capture the experimentally observed, characteristic change in the activation energy of the diffusion process, occurring at the order-disorder transition to the superionic regime. Finite-size effects on ion diffusion are instead much weaker in alpha-AgI. The thermal conductivity is found generally smaller for smaller cells, where the temperature-independent (Allen-Feldman) regime is also reached at significantly lower temperatures. The finite-size effects on the thermal motion of the non-mobile ions composing the solid matrix follow the simple law that holds for solids. Published under an exclusive license by AIP Publishing.