A capacitive microwave sensor with homogeneous field distribution is presented. It relies on a high-impedance parallel-plate arrangement and a properly positioned guard electrode to mitigate fringing field effects. The distance between the capacitor plates can be as large as their diameter. Such an arrangement allows permittivity measurements of irregularly shaped objects like individual biological cells. This is demonstrated with a microchip sensor in a microfluidic setup. The calibration requires only a single reference fluid.