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The electromagnetic characteristics of a circular metal waveguide with a coaxial cylindrical dielectric insert and a layer of absorbing liquid that fills the space between the insert and the waveguide wall have been studied. The transverse waveguide dimensions are comparable with the wavelength. Dependences of the attenuation and phase coefficients of waveguide modes on the structure size and material properties of the layers are found by solving the boundary value problem. It is shown that based on the proposed layered waveguide with the HE11 type of wave, a measuring cell can be designed to work at either fixed frequency with high differential sensitivity or in the frequency range of the single-mode waveguide operation. The cell is of class of cells with calculable geometry. In this case, a reference liquid with known dielectric properties is not required for absolute measurements of the complex permittivity (CP) of the absorbing liquid. The method of finding the CP of absorbing liquids are verified using electromagnetic modeling with CST Microwave Studio. [ABSTRACT FROM PUBLISHER]