Airflow perforations in shielding enclosures can act as apertures facilitating the coupling from internal sources to external electromagnetic interference (EMI). This EMI radiation for single- and dual-screen configurations was studied herein experimentally and with finite-difference time-domain (FDTD) modeling. A general EMI reduction of more than 20 dB was achieved for dual-perforated screens spaced 1 cm apart when compared to EMI for a single perforated screen. However, in the dual-screen case, the space between the screens can act as a thin cavity, which, in turn, can lead to significant radiation at distinct angles. Damping the resonances by loading the space between the screens with lossy material mitigates this problem and achieves more than 20-dB reduction over a single screen.