A method of determining the relative constitutive parameters (µr, εr) is given. This method is based on the Mie solution of a scattering sphere. Field components scattered in two orthogonal planes are measured at 6.17 GHz and 7.03 GHz to calculate the desired parameters of four representative specimen spheres each 1.27 cm in diameter. A consistency process has been developed to reduce random errors caused by theoretical approximations and experimental inaccuracies. Only those data which are considered to have given consistent solutions are then used to produce the material parameters. A target support which can be rotated 360° is used to determine whether a specimen sphere can be assumed homogeneous and isotropic. The present method has in practice no difficult problem of specimen fitting and positioning. Semiquantitative assessments on the final results of (µr, εr) are made for the specimens measured. Usefulness of this method for measuring lossy materials is demonstrated by the use of three lossy specimens. Recommendations for evaluating a unique set of parameters and improving their accuracies are made in both theoretical and experimental aspects.