A device for nondestructive measurements of dielectric loss in substrates of integrated circuits and film materials in a local 2-mm-diameter zone has been developed. The main element of the device is a coaxial resonator with a measurement hole at its end and a clamp for dielectric substrates in the form of a cylindrical waveguide that is evanescent for measurement frequencies. In such a system, emission of electromagnetic waves from the measurement hole is absent, although the phenomenon of emission is characteristic of a coaxial resonator with a hole to which a dielectric is applied. The absence of radiation loss simplifies the determination of the loss tangent for dielectric substrates. A formula for calculations and a measurement technique in the range of 10 GHz are presented.