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A detailed method for determining the dielectric constant of materials using a Ka-band free-space transmission/reflection measurement system is presented. Since the measurement system was designed to minimise the overall cost of the system, correction terms and a smoothing process were necessary to account for limitations in the hardware. The different steps involved in the determination process are explained and their effect on the S-parameters is presented. A through-reflect-match (TRM) free-space calibration method was used, which greatly reduces system errors owing to its simple and stationary nature. The dynamic range of the measurement system after TRM calibration appeared to be better than 50 dB for the reflection coefficient and 29 dB for the transmission coefficient. To determine the unknown dielectric constant of the material, two numerical extraction techniques, a root-finding algorithm and a genetic algorithm were used. Dielectric constant results for a commercially available microwave substrate material sample are presented for both extraction techniques. The difference between the two extraction techniques was <1%. Comparison of the dielectric constant value with measurement performed by a standards testing organisation revealed an agreement within 2%.