We present a dual-frequency electromagnetic scanning probe and apply it for quantitative mapping of the sheet resistance of conducting films. The high-frequency (82 GHz) mode is used for image acquisition, while the low-frequency (5 MHz) mode is used for distance control. We measure magnitude and phase of the near-field microwave reflectivity from conducting films of varying thickness and develop a model which accounts fairly well for our results. This brings us to a quantitative understanding of the contrast in the microwave near-field imaging using an aperture probe, and allows us to achieve quantitative contactless characterization of conducting layers with sheet resistance even below 2 &OHgr;. ©1998 American Institute of Physics.