Estimates of genetic/phenotypic covariances and economic values for slaughter weight, growth, feed intake and efficiency, and three potential methane traits were compiled to explore the effect of incorporating methane measurements in breeding objectives for cattle and meat sheep. The cost of methane emissions was assumed to be zero (scenario A), A$476/t (based on A$14/t CO equivalent and methane's 100-yr global warming potential [GWP] of 34; scenario B), or A$2,580/t (A$30/t CO equivalent combined with methane's 20-yr GWP of 86; scenario C). Methane traits were methane yield (MY; methane production divided by feed intake based on measurements over 1 d in respiration chambers) or short-term measurements of methane production adjusted for live weight (MPadjWt) in grazing animals, e.g., 40-60 min measurements in portable accumulation chambers (PAC) on 1 or 3 occasions, or measurements for 1 wk using a GreenFeed Emissions Monitor (GEM) on 1 or 3 occasions. Feed costs included the cost of maintaining the breeding herd and growth from weaning to slaughter. Sheep were assumed to be grown and finished on pasture (A$50/t DM). Feed costs for cattle included 365 d on pasture for the breeding herd and averages of 200 d postweaning grow-out on pasture and 100 d feedlot finishing. The greatest benefit of including methane in the breeding objective for both sheep and cattle was as a proxy for feed intake. For cattle, 3 GEM measurements were estimated to increase profit from 1 round of selection in scenario A (no payment for methane) by A$6.24/animal (from A$20.69 to A$26.93) because of reduced feed costs relative to gains in slaughter weight and by A$7.16 and A$12.09/animal, respectively, for scenarios B and C, which have payments for reduced methane emissions. For sheep, the improvements were more modest. Returns from 1 round of selection (no methane measurements) were A$5.06 (scenario A), A$4.85 (scenario B), and A$3.89 (scenario C) compared to A$5.26 (scenario A), A$5.12 (scenario B), and A$4.72 (scenario C) for 1 round of selection with 3 PAC measurements. Including MY in the selection index was less profitable because it did not reduce feed costs relative to weight gain. Consequently, for strategies measuring MY but not MPadjWt (and with no estimate of feed intake in the production environment), proportionately greater emphasis was placed on increasing slaughter weight, and as a result, the decreases in methane emissions per animal and per unit of feed intake were smaller than for strategies that measured MPadjWt.