The international shipping sector is a vital part of the global trading system but also a large emitter of carbon dioxide emissions. In the absence of a multilateral carbon policy for the shipping sector, different countries are starting to impose unilateral measures to decarbonize maritime trade. This paper investigates the impact of unilateral policy on global carbon emissions and welfare by introducing heterogeneous transport technology to a quantitative model of trade. The framework emphasizes the role of transport providers which allocate clean and dirty vessels to shipping routes and thereby determine trade flows, transport costs and emissions in the entire network. Unilateral policy interferes with the allocation process by altering the cost of transport or restricting port access to specific vessel types. Using unique data on ship-level fuel consumption and network traffic, I study the impact of upcoming unilateral policy in the EU. I find that carbon taxes can achieve sizeable emission savings as long as the supply of transport services is sufficiently elastic. Emission savings, however, are not large enough to compensate for lower levels of trade, resulting in an aggregate loss of welfare.