We conducted a theoretical investigation of second harmonic generation and other nonlinear features that result from the magnetic Lorentz force, when a single aperture is cut on a thick, opaque palladium substrate. We studied the dependences of linear pump transmission and second harmonic generation near resonance conditions, and explored the different physical mechanisms and their dependences, for example, geometrical features. We found that it is possible to exploit field localization and surface plasmon generation to enhance second harmonic generation in the regime of extraordinary transmittance of the pump field. Both transmitted and backward second harmonic generation conversion efficiencies were investigated. The results reveal that it may be possible to access several potential new applications. In particular, we demonstrated that the exploitation of a combination of nonlinear effects and enhanced transmission makes possible a palladium-based device suitable for H2-leak-detection.