A Monte Carlo simulation of a prototype of PADME’s Small-Angle Calorimeter has been implemented on Geant4. Particular attention has been given to the energy and time resolutions of the distribution of Cherenkov photons produced in a $PbF_2$ crystal and converted into photo-electrons through a PMT photocathode and their dependence on the crystal geometry. I will present the resulting characterization of a single $PbF_2$ crystal’s performance. This talk is based on arXiv:1809.10840.