Several techniques for measuring accurately the complex permittivity of ceramics using a Fabry-Perot resonator have been developed in millimeter frequency range. Accurate measurement became possible at 40-60 GHz by the three new techniques: 1. exact centering of the sample; 2. exact determination of the sample normal direction parallel to the resonator axis using a laser beam; 3. reduction of the higher-order spurious modes. The relative permittivity, /spl epsi/, and dielectric loss tangent, tan /spl delta/, were measured for commercially available silica substrates. It was found that the value of /spl epsi/ was 3.80, independent of frequency, which is consistent with the general feature of fine ceramics with high purity. The measurement error of /spl epsi/ was /spl plusmn/0.5%.