This paper reports heritability estimates for methane traits and genetic relationships with production traits in beef cattle. Traits recorded during the methane test period included dry matter intake (DMI), test liveweight (TWT), methane production (MPR) and methane yield (MY; MPR/DMI). Two methods of calculating residual methane traits (RMP) were evaluated. Production traits included birth (BWT), weaning (WWT), yearling (YWT) and final (FWT) liveweight. Heritabilities for MPR, MY and RMP traits were moderate (0.19 to 0.27), indicating that there is potential to use genetic improvement to reduce methane emissions in Australian beef cattle. MPR was moderately genetically correlated with MY (0.50) and RMP traits (0.50 to 0.63). However, MPR was also moderately to highly genetically correlated (0.36 to 0.86) with weight traits. Methane yield and RMP traits, however, were lowly to moderately genetically correlated (-0.06 to 0.45) with weight traits. These results indicate that selection for lower MPR would have a negative impact on growth in beef cattle. Selection for reduced MY or RMP, however, would lead to reduced MPR with minimal impact on animal productivity. The use of a ratio trait, like MY, in animal breeding is generally undesirable, thus selection on RMP traits is a better alternative.