Scanning microwave microscopy (SMM) is a combination of an atomic force microscope with a vector network analyzer (VNA) to measure locally resolved impedances. The technique finds application in the realms of semiconductor industries, material sciences, or biology. To determine quantitative material properties from the measured impedances, the system must be calibrated. Transferring the calibration from the calibration substrate onto the material under test is strongly limited when using unshielded probes, as the electromagnetic coupling to the surroundings can reach several centimeters. This work reports the fabrication of coaxially shielded probes for a scanning microwave microscope and their integration into such an instrument. We discuss a calibration method with dielectric references, using a simulation-assisted 1-port VNA calibration algorithm. Uncertainty considerations of the measurement process are included and propagation throughout the algorithm is performed. The calibration is verified with an additional dielectric reference. As an application example, the results for a static-random-access memory sample are presented. We identified system-related drift and trace noise as the dominant contributors to the uncertainties of the calibrated results. The here presented shielded tips can broaden the application scope of SMM, as they are door-openers for measurements in liquids.