Herein, we apply a plasmonic near-field scanning nanoscope using a resonant ridge aperture to measure the thickness of a metal thin film. We determine an appropriate design for the resonant ridge aperture to obtain a high dynamic range and sensitivity for the measurement. As a proof of concept, we measure the thickness of gold thin films with thicknesses ranging between 5 and 30 nm. We demonstrate that the experimental and calculated results are in good agreement with one another. Also, we find that any observed errors are caused by uncertainties in the material properties of the metal and by tolerances in the fabrication of the ridge aperture. By comparing these thickness measurements with those taken with atomic force microscopy, we are able to obtain an uncertainty of for our thickness measurements. Regarding the spatial resolution, theoretical analysis indicates that the thickness of a metal thin film should be detectable below 40 nm.