A waveguide method is developed to study the materials with relatively large dielectric constants at microwave range. Basically, the method is similar to the previous waveguide methods represented by short-circuit line and transmission/reflection measurement methods. However, the complex permittivity is not determined by the shift in resonance frequencies, but by numerical analysis of measured scattering parameters. In order to enhance microwave penetration into the specimen with relatively large permittivity, a dielectric plate with lower permittivity is employed for impedance matching. The influences of air gap between the specimen and waveguide wall are evaluated, and the corresponding errors are estimated. The propagation of higher order modes is also considered. Experimental results for several reference ceramics are presented.