Because of economic growth and a strong increase in global energy demand the demand for fossil fuels and therefore also greenhouse gas emissions are increasing, although climate policy should lead to the opposite effect. The coal market is of special relevance as coal is available in many countries and often their first choice to meet energy demand. In this paper we assess possible interactions between climate policies and the global steam coal market. Possible market adjustments between demand centers through market effects are investigated with a numerical model of the global steam coal market until 2030: the "COALMOD-World" model. The COALMOD-World model is an equilibrium model that computes future trade flows, infrastructure investments and prices until 2030. We investigate three specific designs of climate policy: a unilateral European climate policy, an Indonesian export-limiting policy and a carbon capture and storage (CCS) fast-roll out policy in the broader context of climate policy and market constraints. We find that market adjustment effects in the coal market can have significant positive and negative impacts on the effectiveness of climate policies.