A technique for measuring the constitutive parameters of materials over a broad range of frequencies is developed in this work. The technique is specifically designed for planar samples. Planar samples can be placed in the measurement fixture without any special preparation; this makes the technique more convenient than other techniques which require that the sample be machined to fit into a measurement fixture. The finite element method is used in the analysis of the fixture. Using fourth-order elements, the finite element method provides a general, very accurate solution. The technique is experimentally verified by measuring the constitutive parameters of two materials with known properties. The measured results are compared to those of other investigators and are shown to be in good agreement.