  Resonance spectra of two-dimensional dielectric microwave resonators of
circular and square shapes have been measured. The deduced length spectra of
periodic orbits were analyzed and a trace formula for dielectric resonators
recently proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)] was
tested. The observed deviations between the experimental length spectra and the
predictions of the trace formula are attributed to a large number of missing
resonances in the measured spectra. We show that by taking into account the
systematics of observed and missing resonances the experimental length spectra
are fully understood. In particular, a connection between the most long-lived
resonances and certain periodic orbits is established experimentally.
