We demonstrate a technique for contactless mapping of resistivity or dielectric constant of surfaces and films with a spatial resolution better than 100 μm. This technique may be used for the nondestructive testing of semiconducting wafers, conducting polymers, oxide superconductors, and printed circuits. The principle of operation consists of the scanning of a tiny millimeter-wave antenna at a very small height above an inhomogeneous conducting surface and measuring the intensity and phase of the reflected (transmitted) wave. We use a specially designed resonant slit antenna and achieve subwavelength spatial resolution of λ/50.