We describe a near-field scanning microwave microscope which uses a high-quality dielectric resonator with a tunable screw. The operating frequency isf= 4.5 GHz. The probe tip is mounted in a cylindrical resonant cavity coupled to a dielectric resonator. By tuning the tunable screw coming through the top cover, we could improve sensitivity, signal-to-noise ratio, and spatial resolution to better than 1.5 Jim. To demonstrate the ability of local microwave characterization, the surface resistance of metallic thin films has been mapped.