We present a general method for designing XUV aperiodic multilayer mirrors that can mimic a given target spectrum, specifically, the spectral transmission of an XUV optical system. The method is based on minimizing a merit function and using fidelity parameters that quantify the matching of the multilayer reflectivity spectrum with that of the target spectrum. To assess the feasibility of fabricating such a system, we show how to reduce the layer-to-layer thickness variations throughout the aperiodic layer stack. We demonstrate the design method using an example of an EUV optical system composed of 12 identical Mo/Si multilayer mirrors having a reflectivity peak at 13.5 nm. We found that the target spectrum can be mimicked with high fidelity either with a single reflection at an aperiodic multilayer mirror combined with standard absorbing filters or, if required, with two subsequent reflections at a mimic mirror. These examples demonstrate the applicability for metrology at XUV sources, including spectrally proper source imaging. Because our approach is of general applicability, the process can be used to mimic any other narrowband, single-peaked target spectrum in the XUV region.