We report experimental observations and numerical simulations of second and third harmonic generation from a gold nanograting, which exhibits a plasmonic resonance in the near infrared. The resonance is tunable, with a spectral position that depends on the angle of incidence. All things being equal, the enhancement of nonlinear optical processes produced by the field localization in the nanograting when compared with a flat gold mirror manifests itself dramatically from the ultraviolet to the visible range: second harmonic generation conversion efficiencies increase by more than three orders of magnitude, while we report a third harmonic generation conversion efficiency enhancement factor of 3200, both in excellent agreement with our theoretical predictions. The clear inferences one may draw from our results are that our model describes the dynamics with unprecedented accuracy and that much remains to be revealed in the development of nonlinear optics of metals at the nanoscale.