This thesis deals with the computation of electromagnetic fields in complex, superconducting resonators, as well as the efficient calculation of the losses of such resonances by the couplers and beampipes. A perturbation approach is used to efficiently assemble the resulting nonlinear eigenvalue problem, which is then solved by using the Newton method. Using the proposed methods, current research questions for the Third Harmonic Module of the FLASH accelerator, the bERLinPro mainlinear accelerator and the BESSY VSR cavity-design are be answered.<eng>
