Trade policy is often cast as a solution to the free‐riding problem in international climate agreements. This paper examines the extent to which trade policy can deliver on this promise. We incorporate global supply chains of carbon and climate externalities into a multi‐country, multi‐industry general equilibrium trade model. By deriving theoretical formulas for optimal carbon and border taxes, we quantify the maximum efficacy of two trade policy solutions to the free‐riding problem. Adding optimal carbon border taxes to existing tariffs proves largely ineffective, delivering only 3.4% of what could be achieved under globally optimal carbon pricing. In contrast, Nordhaus's (2015) climate club framework, in which border taxes are used as contingent penalties to deter free‐riding, can achieve 33–68% of the globally optimal carbon reduction, depending on the initial coalition (EU, EU + US, or EU + US + China). In all cases, the climate club ensures universal compliance, thereby preserving free trade.