We demonstrate the possibility of estimating in a simple way the expected frequency of the resonant response to an external electromagnetic field in a thin golden nanoantenna having a rectangular cross section. The paper considers nanoantennas with a thickness smaller than the thickness of the skin layer or comparable with it. Analytical expressions for estimating the resonance response are presented, and full-wave simulation is performed. The algorithm for obtaining such estimates is important, in particular, for planning experiments without using full-wave simulation, which is often rather resource consuming. To obtain analytical expressions, a refined LCR circuit model is used. The analytical estimates obtained for the characteristics of the resonant response are in good agreement with the results of the full-wave simulation.