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 non-monotonic, but is weakly increasing in the tax rate under linear taxation if each worker has negative non-pecuniary 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.