I examine how federal and state courts influence the relationship between state-level public opinion and policy. The system of dual federalism, combined with the sweeping power of judicial review, allows state and federal courts to establish the types of policies that states are constitutionally allowed to implement. In particular, federal courts can set "federal floors" for policy, below which no state can go. State courts, in turn, can raise the level of this floor. As a result, both federal and state courts can shape the extent to which state policy can match the preferences of the median voter in a given state. I demonstrate this important role of courts by analyzing data on public opinion, judicial decisions, and state-level policy on the issue of abortion, from 1973 to 2012. I show that changes in the set of allowable abortion restrictions, according to the combined decisions of federal and state courts, significantly affect whether states implement majority-preferred policies. These results demonstrate the importance of placing courts in the larger study of state-level representation.