This work focuses on the study of shield systems consisting of nested enclosures. In the first step, using FDTD simulations and measurements in an anechoic chamber, we investigate the shielding effectiveness (SE) of the system of two nested rectangular enclosures in the frequency range of up to 3 GHz. It is shown for the first time that for a number of frequencies, the SE of the nested shields can be improved by 40–50 dB due to the asymmetric arrangement of the enclosures, their electrical connection, and the mutually perpendicular arrangement of the apertures. Next, we analyze the emissions from the electromagnetic radiation sources in the presence and absence of a nested shield system. The results show that a nested shield system may not attenuate the emission amplitude but increases it by more than 58 dB at the resonant frequencies of the enclosures. Then, we prove that a single enclosure can have a higher SE than the same enclosure as a part of a poorly designed nested shield system. The final part of the article formulates practical recommendations for the design of nested shield configurations.