We have a condensed matter analog of the Higgs mechanism. Colloquially, we say the gauge boson — in this case, the photon — "eats up" the Goldstone boson — in this case, plasmons built up from a condensate of Cooper pairs — giving rise to a new quasiparticle. Unlike photons, this quasiparticle has an energy gap in the dispersion relation. This is the condensed matter analog of a massive vector boson. Unlike a photon, this quasiparticle can have zero velocity, for instance.
It's also true that if the energy of the photon before it reaches the superconductor is less than the energy gap, this photon will be reflected. If the initial energy is larger, we have a superposition of a transmitted and a reflected component for the wave function.
Edit: When it comes to practical issue, it's even more impressive: the superconducting mirror was the key experimental ingredients in the Haroche, Raymond and Brune experiment, see e.g. http://arxiv.org/abs/quant-ph/0612031 and http://arxiv.org/abs/0707.3880 for the first experimental proofs of the birth and death of a photon inside a cavity made with superconducting mirror. This experiment earned the 2012 Nobel Prize, see http://www.nobelprize.org/nobel_prizes/physics/laureates/2012/. Without the ultra-high reflexion coefficient of the superconducting mirror (for microwave radiations), these experiments would not have been possible.