Quantitative dielectric and conductivity mapping in the nanoscale is highly desirable for many research disciplines, but difficult to achieve through conventional transport or established microscopy techniques. Taking advantage of the micro-fabrication technology, we have developed cantilever-based near-field microwave probes with shielded structures. Sensitive microwave electronics and finite-element analysis modeling are also utilized for quantitative electrical imaging. The system is fully compatible with atomic force microscope platforms for convenient operation and easy integration of other modes and functions. The microscope is ideal for interdisciplinary research, with demonstrated examples in nano electronics, physics, material science, and biology.