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This paper presents a method of performing microwave characterizations of nematic liquid crystals using a circular patch resonator and finite-element software. This technique, which is based on inferring material properties from measured resonances, was demonstrated with BL006 (a nematic liquid-crystal mixture) over the frequency range of 4.8-8.7 GHz. The resonator comprises a thin liquid-crystal sample between a ground plane and a directly coupled inverted patch. The coupling-line design minimizes resonator loading and reflections from substrate impedance discontinuities, and the liquid crystal is aligned with rubbed surfaces and low-frequency voltages. The permittivity is found with simulations that iteratively narrow the difference between the measured and computed resonances. The computed values for BL006 agree well with those found in the literature. This method benefits from simple resonator construction, straightforward simulations, and accuracy that derives from the finite element's detailed modeling of coupling and geometry of the fabricated device.