We describe the effects of disorder on the coherence properties of a 2×2 array of Josephson junctions (a ‘‘plaquette’’). The disorder is introduced through variations in the junction characteristics. We show that the array will remain one‐to‐one frequency locked despite large amounts of the disorder, and determine analytically the maximum disorder that can be tolerated before a transition to a desynchronized state occurs. Connections with largerN×Marrays are also drawn. ©1995 American Institute of Physics.