Accurate measurements of the microwave surface resistance (Rs) of high temperature superconductor (HTS) films are important with regard to applications of HTS materials for wireless communications. As the surface resistance values of HTS films are usually extracted from the measured unloaded quality factor ($Q_0$) of resonators made of HTS films, it is essential to measure the resonator $Q_0$ with accuracy. The $TE_{011};mode;Q_0$ of sapphire resonators with the endplates made of $YBa_2Cu_3O_{7-{delta}}$(YBCO) film on $LaAlO_3$ is measured by using the S-parameter circle-fit method at a frequency of about 19.6 GHz and temperatures of 30 K to 90 K, which is compared with the measured values by using the Lorentzian-fit method. Good agreements are found between the two sets of $Q_0$ values measured by using the two different methods whether the resonator is used in a weak-coupling scheme or a strong-coupling scheme, showing reliability of both methods fur measuring the resonator $Q_0$ accurately. The $Q_0$ of sapphire resonators with a gap between the top plate and the rest of the resonator is also discussed.