Policy analysis with potentially misspecified dynamic stochastic general equilibrium (DSGE) models faces two challenges: estimation of parameters that are relevant for policy trade-offs and treatment of estimated deviations from the cross-equation restrictions. This paper develops and explores policy analysis approaches that are either based on a generalized shock structure for the DSGE model or the explicit modelling of deviations from cross-equation restrictions. Using post-1982 U.S. data we first quantify the degree of misspecification in a state-of-the-art DSGE model and then document the performance of different interest-rate feedback rules. We find that many of the policy prescriptions derived from the benchmark DSGE model are robust to the various treatments of misspecifications considered in this paper, but that quantitatively the cost of deviating from such prescriptions varies substantially.