Economic evaluation of climate policy traditionally treats uncertainty by appealing to expected utility theory. Yet our knowledge of the impacts of climate policy may not be of sufficient quality to justify probabilistic beliefs. In such circumstances, it has been argued that the axioms of expected utility theory may not be the correct standard of rationality. By contrast, several axiomatic frameworks have recently been proposed that account for ambiguous beliefs. In this paper, we apply static and dynamic versions of a smooth ambiguity model to climate mitigation policy. We illustrate via comparative statics the conditions under which an increase in ambiguity aversion increases the optimal level of mitigation in some simple examples. We then extend our analysis to a more realistic, dynamic setting, and adapt a well-known empirical model of the climate-economy system to show that the value of emissions abatement increases as ambiguity aversion increases, and that this "ambiguity premium" can in some plausible cases be very large.