An effective matched design must achieve several goals: for instance, balancing covariate distributions marginally, ensuring paired units are similar on key covariates, and forming sufficiently many pairs. Yet these goals may come into conflict with one another, so that optimizing one forces a less desirable result on another. We address the issue by studying matched designs that are Pareto-optimal with respect to two goals. We articulate how Pareto-optimal sets provide full descriptions of tradeoffs between two generalized matching goals, and provide efficient methods for computing a representative subset of the Pareto-optimal set. We illustrate the practical utility of the method in reanalysis of a large surgical outcomes study comparing outcomes of patients treated by US-trained surgeons and of patients treated by internationally-trained surgeons. We evaluate the cost of balancing an important variable excluded from the original match in terms of two other design goals, average closeness of matched pairs on a multivariate distance and size of the final matched sample.