We analyze the effects of taxation in two-sided matching markets where agents have heterogeneous preferences over potential partners. Our model provides a continuous link between models of matching with and without transfers. Taxes generate inefficiency on the allocative margin, by changing who matches with whom. This allocative inefficiency can be nonmonotonic, but is weakly increasing in the tax rate under linear taxation if each worker has negative nonpecuniary utility of working. We adapt existing econometric methods for markets without taxes to our setting, and estimate preferences in the college-coach football market. We show through simulations that standard methods inaccurately measure deadweight loss.