SUMMARYWe describe a method for simultaneously measuring the complex permittivity and the complex permeability of a lossy sheet that is inserted between two flanged rectangular waveguides. The equivalence principle of the electromagnetic fields is applied to the boundary surfaces between the sheet and the waveguides to derive the integral equations while taking the high-order modes excited at the boundary surfaces into account. Then the method of moments is used in these equations to formulate the direct problem. Newton's method is applied to the inverse problem, and the convergence performance of the solution is examined. Furthermore, the reflection coefficients and the transmission coefficients are measured for some samples, and their complex permittivities and complex permeabilities are estimated from these coefficients.