Multiresolution analysis or wavelet analysis provides a toolbox not only for signal processing, but also for synthesis of complex systems. Wavelets can be used for modeling complex parts of microwave circuits, such as cavity resonators. The differential equations describing the physical behavior of the device can be discretized using multiple resolutions simultaneously, i.e., high resolutions, where the details of the geometry demand it, and low resolutions, where the geometry is smooth. Using wavelet analysis offers the possibility of systematic and adaptive refinement, where the result is not sufficiently precise. Our method gives an approximation for the error of the solution in order to make it possible to decide, whether refinements are necessary.