The postresonator method proposed by Hakki and Coleman for the measurement of dielectric properties of solids in the microwave region is reexamined. Based on the experiments performed around 10 GHz, the limitations of the method in loss determination for materials with tan delta < 5 x 10(-4) are outlined. Alternative techniques for studying high-Q materials are described. Loss measurements performed on well-prepared ceramics have been used to draw comparisons among these techniques. Some of the experimental findings are new and are reported for the first time.