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Using WGM resonators allow achieving high accuracy in determining the substances permittivities due to the high Q-factor. The resonator with a microfluidic channel is promising for the study of small-volume liquids, which is especially important for bioliquids. In a Ka-band a sapphire resonator with microfluidic channel has been proposed as a measurement cell, but in the sub-THz range a quartz resonator has more suitable characteristics due to its high Q-factor. In the paper we propose a measurement cell for the determination of complex permittivity of liquids in sub-THz range on the basis of quasi-optical quartz resonator with a layer of plastic comprising a microfluidic channel. Experimental studies of the resonator structure are carried out and a model for numerical research in the software COMSOL Multiphysics is proposed. By means of c omparing the resonator frequencies and Q-factors values with the corresponding values obtained with the numerical model the correction of the model has been carried out for the water-filled microfluidic channel. It is shown that the model for numerical studies correctly describes the resonator structure. The values of the resonator frequency and Q-factor obtained experimentally and numerically, for the microfluidic channel filled with the substances with well-known complex permittivity (methanol, propanol, ethanol, acetone), are in good agreement, which indicates the possibility of using the resonator as a measurement cell allowing the research on small-liquid permittivity using the special calibration procedure.