Superradiance occurs in quantum optics when the emission rate of photons from multiple atoms is enhanced by inter-atom interactions. When the distance between two atoms is comparable to the emission wavelength, the atoms become entangled and their emission rate varies sinusoidally with their separation distance due to quantum interference. We here explore a theoretical model of pilot-wave hydrodynamics, wherein droplets self-propel on the surface of a vibrating bath. When a droplet is confined to a pair of hydrodynamic cavities between which it may transition unpredictably, in certain instances the system constitutes a two-level system with well-defined ground and excited states. When two such two-level systems are coupled through an intervening cavity, the probability of transition between states may be enhanced or diminished owing to the wave-mediated influence of its neighbour. Moreover, the tunneling probability varies sinusoidally with the coupling-cavity length. We thus establish a classical analog of quantum superradiance.