The European Union (EU) has agreed to gradually include shipping in the EU emissions trading scheme (EU ETS), which makes shipping companies vulnerable to carbon price fluctuations. The aim of this paper is to investigate the effectiveness of carbon and petroleum futures contracts in managing carbon and bunker risks. We examine the effectiveness of alternative hedging methods, including both static and dynamic approaches, to estimate optimal hedge ratios under single and composite cross-hedge settings. Our results show that carbon future contracts are important for hedging the carbon emission allowances price risk, and Brent oil futures are the most effective instrument for out-of-sample hedging of bunker prices. In addition, the hedging effectiveness indicates that conventional methods outperform the sophisticated models in terms of variance reduction. Our study offers new insights into how the carbon and bunker markets relate to a combination hedging in reducing the joint price risk, which can be used to promote risk management in the market.