In this paper the relations between the errors in measurements for the microwave surface resistance of a high-temperature superconducting thin film and the geometry and frequency of a parallel plate dielectric resonator were analyzed. The results showed that the influence of the 2a/L(ratio of the diameter of the dielectric rod to its length), the b/a (ratio of the radius of the metal cavity to the radius of the dielectric rod) and the frequency f on the error and the measurable minimum surface resistance Rsmin is quite important. The curves obtained in this paper could be used to design the dielectric resonators of parallel plate type. The error of order of 1% and Rsmin of the order of micro-ohm could be obtained by proper choosing 2a/L, b/a and f.