This paper analyzes the mitigation of enteric methane (CH4) emissions from ruminants with the use of feed additives inhibiting of rumen methanogenesis to limit global temperature increase to 1.5 °C. A mathematical simulation conducted herein predicted that pronounced inhibition of rumen methanogenesis with pure chemicals or bromoform-containing algae can contribute to limit global temperature increase by 2050 to 1.5 °C only if widely adopted at a global level and considering an efficacy higher than obtained in most studies. Currently, the most important limitations to the adoption of antimethanogenic feed additives are probably increased feeding cost without a consistent return in production efficiency, and achieving sustained delivery of inhibitors to the rumens of non-supplemented, extensively ranging animals. Economic incentives, and changes in rumen microbial metabolism caused by inhibiting methanogenesis, could potentially be used to make the methanogenesis inhibition intervention cost effective. Also, the composition of the methanogenic community, and rate of disappearance of inhibitors of methanogenesis in the rumen can influence the effective dose of the inhibitors, and hence the cost of their adoption. Possible means for sustained delivery of antimethanogenic compounds to extensively grazing animals are discussed. Limitations and knowledge gaps of these approaches, and future research directions, are examined.