This paper studies the behavior of a central bank that seeks to conduct policy optimally while having imperfect credibility and harboring doubts about its model. Taking the Smets-Wouters model as the central bank’s approximating model, the paper’s main findings are as follows. First, a central bank’s credibility can have large consequences for how policy responds to shocks. Second, central banks that have low credibility can benefit from a desire for robustness because this desire motivates the central bank to follow through on policy announcements that would otherwise not be time-consistent. Third, even relatively small departures from perfect credibility can produce important declines in policy performance. Finally, as a technical contribution, the paper develops a numerical procedure to solve the decision-problem facing an imperfectly credible policymaker that seeks robustness.