The dielectric constant varies with frequency so that the known dielectric constant at low-frequency is no longer valid at high-frequency regions. When the frequency increases, experimental imperfection can significantly affect to determine the dielectric constant in the resonator-based measurement setup, which may mislead the estimated dielectric constant. In contrast to the existing method using a fundamental TE10 mode in a rectangular waveguide, we propose to use a TE01 mode in a circular waveguide which may not be affected by the experimental imperfection such as an air gap between the surface of the waveguide and the dielectric material. We present the experimental result of the proposed measurement method and its analysis by means of simulations.