We theoretically investigate second harmonic generation that originates from the nonlinear, magnetic Lorentz force term
from single and multiple apertures carved on thick, opaque metal substrates. The linear transmission properties of
apertures on metal substrates have been previously studied in the context of the extraordinary transmission of light. The
transmission process is driven by a number of physical mechanisms, whose characteristics and relative importance
depend on the thickness of the metallic substrate, slit size, and slit separation. In this work we show that a combination
of cavity effects and surface plasmon generation gives rise to enhanced second harmonic generation in the regime of
extraordinary transmittance of the pump field. We have studied both forward and backward second harmonic generation
conversion efficiencies as functions of the geometrical parameters, and how they relate to pump transmission efficiency.
The resonance phenomenon is evident in the generated second harmonic signal, as conversion efficiency depends on the
duration of incident pump pulse, and hence its bandwidth. Our results show that the excitation of tightly confined modes
as well as the combination of enhanced transmission and nonlinear processes can lead to several potential new
applications such as photo-lithography, scanning microscopy, and high-density optical data storage devices.