Si-based nanomaterials are a promising platform for nonlinear optics due to the central crystal symmetry breaking at the nanoscale. In this work, we studied the second harmonic generation (SHG) in spherical mesoporous nanocrystalline Si/SiO2 nanoparticles deposited on a gold substrate, combining experimental measurements and numerical simulations. The performed theoretical analysis showed that SHG signal related to Si crystallites is dominant in nonlinear response from Si/SiO2 nanoparticles. Our investigation revealed that Mie resonances in the mesoporous nanoparticles and their interaction with the gold substrate influence SHG efficiency. Moreover we observed additional enhancing of SHG efficiency at specific wavelengths, caused by constructive interference between resonances of the different orders. Experimentally measured SHG spectra for mesoporous nanoparticles matched well with results of our calculations. These findings demonstrate the potential of mesoporous nanocrystalline Si/SiO2 nanoparticles as efficient tunable frequency converters for nonlinear optical applications.