Methods of reducing methane emission in one or more ruminant animals, while simultaneously avoiding nitrate intoxication, are disclosed. The methods may include feeding the ruminant animal(s) a feed including a slow-release ruminant feed additive, where the slow release of nitrate ion from the feed additive keeps the overall levels of released nitrate in the rumen below a level that would result in nitrate intoxication, yet provides a level of non-protein nitrate ion to ruminant bacteria high enough to act as an antimethanogenic agent, resulting in a reduced production of methane. The slow-release ruminant feed additive may be in a granular or round form and encapsulated by a coating. The feed additive may include 40% to 85% in weight nitrate ion, 0% to 50% in weight sulfur, 1% to 40% in weight of a coating including hydrogenated vegetable fat; and 0% to 20% of additives in weight.