Methane is a greenhouse gas of high interest to the dairy industry, with 57% of Australia's dairy emissions attributed to enteric methane. Enteric methane emissions also constitute a loss of approximately 6.5% of ingested energy. Genetic selection offers a unique mitigation strategy to decrease the methane emissions of dairy cattle, while simultaneously improving their energy efficiency. Breeding objectives should focus on improving the overall sustainability of dairy cattle by reducing methane emissions without negatively affecting important economic traits. Common definitions for methane production, methane yield, and methane intensity are widely accepted, but there is not yet consensus for the most appropriate method to calculate residual methane production, as the different methods have not been compared. In this study, we examined 9 definitions of residual methane production. Records of individual cow methane, dry matter intake (DMI), and energy corrected milk (ECM) were obtained from 379 animals and measured over a 5-d period from 12 batches across 5 yr using the SF tracer method and an electronic feed recording system, respectively. The 9 methods of calculating residual methane involved genetic and phenotypic regression of methane production on a combination of DMI and ECM corrected for days in milk, parity, and experimental batch using phenotypes or direct genomic values. As direct genomic values (DGV) for DMI are not routinely evaluated in Australia at this time, DGV for FeedSaved, which is derived from DGV for residual feed intake and estimated breeding value for bodyweight, were used. Heritability estimates were calculated using univariate models, and correlations were estimated using bivariate models corrected for the fixed effects of year-batch, days in milk, and lactation number, and fitted using a genomic relationship matrix. Residual methane production candidate traits had low to moderate heritability (0.10 ± 0.09 to 0.21 ± 0.10), with residual methane production corrected for ECM being the highest. All definitions of residual methane were highly correlated phenotypically (>0.87) and genetically (>0.79) with one another and moderately to highly with other methane candidate traits (>0.59), with high standard errors. The results suggest that direct selection for a residual methane production trait would result in indirect, favorable improvement in all other methane traits. The high standard errors highlight the importance of expanding data sets by measuring more animals for their methane emissions and DMI, or through exploration of proxy traits and combining data via international collaboration.