Our partners at TU Darmstadt are investigating, within this consortium, a novel technique for depositing a Nb3Sn thin film on superconducting radio-frequency (SRF) cavities using magnetron sputtering. However, imperfections in the coating can lead to a loss of superconductivity. In this project, we will develop fast numerical methods to characterize the electromagnetic behavior of the coated cavities, while modeling the roughness of the coated surface at high resolution. To this end, we will use the boundary element method to avoid a computationally expensive volumetric discretization of the cavities. The resulting methods will be used to understand how coating imperfections affect the performance of an SRF cavity and to what extent imperfections in the thin film can be tolerated without compromising functionality.