In this study, the Hilbert-Huang Transform (HHT) and other frequency analysis methods, Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT), are employed to numerically analyze electromagnetic phenomena with strong non-linearity. In the numerical experiments, electromagnetic wave propagation simulations using the Finite-Difference Time-Domain (FDTD) method are performed to reproduce the behavior of electromagnetic shielding effects leaking from the shielding plate. The obtained results were analyzed using the HHT, STFT, and CWT methods; the HHT analysis showed that electromagnetic waves around the input wavelength 2.45 GHz leak significantly from the shielding plate. On the other hand, the STFT did not accurately resolve the signal, and the CWT unexpectedly showed strong amplitudes in the low-frequency region. These results suggest that HHT performs better in analyzing signals with strong non-linearity and provides more accurate results than other methods.