Natural methane emissions are noticeably influenced by warming of cold arctic ecosystems and permafrost. An evaluation specifically of Arctic natural methane emissions in relation to our ability to mitigate anthropogenic methane emissions is needed. Here we use empirical scenarios of increases in natural emissions together with maximum technically feasible reductions in anthropogenic emissions to evaluate their potential influence on future atmospheric methane concentrations and associated radiative forcing (RF). The largest amplification of natural emissions yields up to 42% higher atmospheric methane concentrations by the year 2100 compared with no change in natural emissions. The most likely scenarios are lower than this, while anthropogenic emission reductions may have a much greater yielding effect, with the potential of halving atmospheric methane concentrations by 2100 compared to when anthropogenic emissions continue to increase as in a business-as-usual case. In a broader perspective, it is shown that man-made emissions can be reduced sufficiently to limit methane-caused climate warming by 2100 even in the case of an uncontrolled natural Arctic methane emission feedback, but this requires a committed, global effort towards maximum feasible reductions.