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The European Parliament has agreed on a target of a 20% share of renewables in the EU's total energy consumption by 2020. To achieve the target, the European Council has adopted mandatory differentiated national targets for each of the member states. In this paper, we consider the use of green certificates to reach the renewable targets and we analyze the potential for cost reductions by allowing for trade in green certificates across member states. We show that differentiated national targets cannot ensure a cost-effective implementation of the overall target for the EU's renewable energy consumption. Trade in green certificates can ensure a cost-effective distribution of renewable energy production, but the national targets prevent a cost-effective distribution of energy consumption. Nevertheless, our numerical model indicates that EU-wide trade in green certificates may cut the EU's total cost of fulfilling the renewable target by as much as 70% compared with a situation with no trade. However, the design of green certificate markets may have a large impact on the distribution of costs across countries.