Increasing dairy farm productivity while simultaneously mitigating greenhouse gases emissions is a common policy goal in many countries. In this paper, we assess trade-offs and synergies between these goals for pasture-based dairy farms in Brazil. We apply stochastic frontier analysis within a translog hyperbolic distance function specification, including methane emissions as an undesirable output and accounting for annual climatic types. Our results indicate that on average, farmers can improve their production by 9.4% while simultaneously reducing methane emissions by 8.7%. The adoption of more productive cows and improved pastures have a positive effect on the environmental efficiency of the farms. Farmers operating in warmer and dryer climate types tend to have lower environmental efficiency. Calculating shadow prices for methane emitted on farms indicates that the mean abatement costs of methane are US $2,254 per tonne. Overall, by reducing inefficiency, dairy farmers can significantly increase farm production while simultaneously reducing emissions and thus contribute to national commitments to eradicate hunger and mitigate methane emissions.