  Eigen oscillations in a superconducting parallel plate resonator with the
Josephson-coupled plates are investigated. While the insulator thickness S
changes from tens of microns down to the decay lengthscale of the
superconducting wavefunction into a dielectric, \xi~1 nm, both the resonant
frequency and Q-factor vary non-monotonically by up to three orders in
magnitude. A crossover between the Swihart waves and Josephson plasmons causes
a global minimum in the resonant frequency and a local maximum in the Q-factor
at S~10\xi.
