We demonstrate the ability of single-subwavelength-size nanoapertures fabricated in a gold metal thin film to enhance second-harmonic generation (SHG) as compared to a bare metal film. Nonlinear microscopy imaging with polarization resolution is used to quantify the SHG enhancement in circular and triangular nanoaperture shapes. The dependence of the measured SHG enhancement on circular aperture diameters is seen to originate from both phase retardation effects and field enhancements at the nanoaperture edge. Triangular nanoapertures exhibit superior SHG enhancement compared with circular ones, as expected from their noncentrosymmetric shape.