Non-destructive evaluation of the permittivity of materials at microwave frequencies requires a set of calibration data. The accuracy of this data is important in the inversion of measurement values to dielectric constants and loss tangents. In this paper, a mathematical method for the interpretation of measurements taken by the open microstrip and open slot resonators is presented. The method is efficient computationally and its high accuracy has been supported experimentally for a rectangular microslrip patch resonator and a slot resonator. Example results including variations of the resonant frequency, return-loss and input impedance with the permittivity are presented and a technique for the inversion of the return-loss (or the input impedance)is demonstrated for low-loss dielectrics. The inversion of measurement results on a perspex taken by a slot resonator show that the dielectric constant obtained is very close to (within 0.5% of) that specified by the manufacturer.