The dielectric resonator (DR) method has been proved to be very useful for accurate measurements of the surface resistance (R-S) of high-T-C superconductor (HTS) films, with the sapphire resonator method having been published as an international standard for the R-S of HTS films. We investigated the effects of electromagnetic waves near the edge of superconductor films on the effective R-S (R-S(eff)) of YBa2Cu3O7-delta (YBCO) films as measured by using the dielectric resonator method. The unloaded quality factor (Q(0)) of the dielectric resonators, with the YBCO films being in direct contact with the Cu ground, was compared with that for the YBCO films separated from the surrounding Cu through a gap at frequencies of similar to 19.5 GHz and 8.5 - 8.7 GHz by using a sapphire resonator and a rutile resonator, respectively. For the two resonators, differences in Q(0) appeared to be within +/-1% regardless of the existence of edge fields in the gap, revealing an insignificant effect of the edge fields on the resonator's Q(0). However, the R-S(eff) of the YBCO films, as determined from the Q(0) of the rutile resonator, appeared to vary up to +/-9 % while little changes in the R-S(eff) of YBCO films were observed due to edge fields for the sapphire resonator. The different variations in the R-S(eff) of YBCO films due to the existence of edge fields between the two resonators S are attributed to the significant differences in the loss tangent values of sapphire and rutile.