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The reflection off an open ended coaxial probe pressed against a material under test is used to determine the complex microwave (1 MHz–20 GHz) dielectric response of the material. A full-wave analysis of the aperture admittance of the probe, in terms of the dielectric properties of the backing material and the dimensions of the experimental geometry, is given. We discuss the calibration procedure of the setup and present the complex dielectric response of several materials determined from the measured reflection coefficient. The results obtained with the open ended coax interpolate well between data taken at lower and higher frequency bands using different experimental methods. We demonstrate that this method can be applied to perform dielectric measurements at cryogenic temperatures. © 2000 American Institute of Physics.