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Due to their large birefringence and moderately low loss, liquid crystals (LCs) are a promising dielectric media for development of a variety of reconfigurable millimeter-wave devices. In order to optimize the design of tunable millimeter-wave devices, accurate values of the dielectric and elastic constants, as well as the loss tangents of LCs, are needed. However, characterization of LCs at millimeter-wave frequencies is a very challenging and demanding task. In this work, a transmission line method is used for the broadband characterization of nematic LCs in the frequency range of 30-60 GHz. For this purpose, a unique LC cell is proposed and using this, five different nematic LCs, including E7, K15, E44, E63, and MDA-00-3506, are measured and the values of their electrical and mechanical parameters are extracted. The extraction of these parameters from the measurements involves an optimization using two finite-element computer programs recently developed by the authors for the prediction of the local alignments of LC molecules and the wave propagation within the test cell. The highest values of the dielectric birefringence and the highest values of the loss tangents are recorded for E44 and MDA-00-3506. The loss tangent for all the LCs shows a general downward trend as the frequency increases, which is a useful characteristic in the development of reconfigurable millimeter-wave devices.