Climate policy is changing fast in the European Union, with country leaders raising the bloc’s ambition to reduce greenhouse gas emissions by 2030 and 2050. However, there is uncertainty about the allocation of decarbonisation effort between EU member states. This paper develops a multi-objective optimisation framework to provide insights to decision makers in this policy context by exploring trade-offs between stronger decarbonisation goals and higher costs. Applying this approach we find that, unless the 2030 policy objective is very ambitious, small changes in emission abatement do not entail large changes in costs. The picture changes when decision-making explicitly accounts for external costs of emissions of greenhouse gases and air pollutants in the optimisation procedure. In this case the costs to comply with a specific 2030 target rise faster the more ambitious the target becomes, but most decisions lead to negative social costs, which means that decarbonisation will be beneficial to the national economy. We also address the required level of investments and public expenditures for implementing specific policy mixes and the attainability of climate neutrality by 2050 as pledged by the EU. Although the modelling framework has been developed for a specific country and is tailored to the specific EU policy circumstances, the proposed methodology is entirely suitable for other world regions with a demanding decarbonisation roadmap.