Reducing enteric methane emissions from agriculture is considered imperative in the short term to stabilise global warming below 1.5 degrees. However, policymakers are faced with multiple and potentially conflicting goals in this pursuit, particularly with food security and conservation of biodiversity. The aim of this paper is to investigate whether there exists a policy response that can ensure the preservation of nature areas, specifically semi-natural pastures (naturbetesmarker), while simultaneously reducing enteric methane emissions from livestock cost-effectively. We perform the analysis with the spatial and dynamic, agent-based model AgriPoliS that is capable of simulating structural change in agriculture in response to radical policy reform, which we extended for methane abatement. Our simulations of the cost-effective solution for increasingly ambitious methane abatement targets, demonstrated that 25 % abatement could be reached with minimal impact on the area of pastures through re-structuring of livestock production and the use of a commercially available feed additive (3-NOP) that suppresses the generation of methane in the rumen. We conclude that technical measures to reduce emissions, such as feed additives, are a promising complementary measure for reducing emissions, but currently farmers have no economic incentive to invest in such low-cost abatement technologies. To avoid loss of nature areas dependent on ruminant grazing, targeted agri-environmental schemes were found to be necessary to preserve these areas in the event of climate action. In this respect agri-environmental payments play a crucial role in strengthening the resilience of agricultural biodiversity to policy measures targeting methane abatement.