We examine sample-to-sample fluctuations in the electrical conductance G of a mesoscopic structure containing superconducting islands and demonstrate that these are consistent with predictions of universal conductance fluctuations in normal disordered solids. For two separate inclusions with order parameter phases phi1 and phi2, the dependence of G on the phase difference is computed. In contrast with a recent prediction for the finite-temperature conductivity of a disordered medium with two superconducting boundaries, we demonstrate that both the conductance of individual samples and the ensemble-averaged conductance vary periodically with period 2pi.