Enteric methane emissions from ruminants account for ∼35% of New Zealand’s greenhouse gas emissions. This poses a significant threat to the pastoral sector. Breeding has been shown to successfully lower methane emissions, and genomic prediction for lowered methane emissions has been introduced at the national level. The long-term genetic impacts of including low methane in ruminant breeding programs, however, are unknown. The success of the New Zealand sheep industry is currently heavily reliant on the prolificacy, fecundity and survival of adult ewes. The objective of this study was to determine genetic and phenotypic correlations between adult maternal ewe traits (live weight, body condition score, number of lambs born, litter survival to weaning, pregnancy scanning and fleece weight), faecal and Nematodirus egg counts and measures of methane in respiration chambers. More than 9,000 records for methane from over 2,200 sheep measured in respiration chambers were collected over 10 years. Sheep were fed on a restricted diet calculated as approximately twice the maintenance. Methane measures were converted to absolute daily emissions of methane measured in g per day (CH4/day). Two measures of methane yield were recorded: the ratio of CH4 to dry matter intake (g CH4/kg DMI; CH4/DMI) and the ratio of CH4 to total gas emissions (CH4/(CH4 + CO2)). Ewes were maintained in the flocks for at least two parities. Non-methane trait data from over 8,000 female relatives were collated to estimate genetic correlations. Results suggest that breeding for low CH4/DMI is unlikely to negatively affect faecal egg counts, adult ewe fertility and litter survival traits, with no evidence for significant genetic correlations. Fleece weight was unfavourably (favourably) correlated with CH4/DMI (rg = −0.21 ± 0.09). Live weight (rg = 0.3 ± 0.1) and body condition score (rg = 0.2 ± 0.1) were positively correlated with methane yield. Comparing the two estimates of methane yield, CH4/DMI had lower heritability and repeatability. However, correlations of both measures with adult ewe traits were similar. This suggests that breeding is a suitable mitigation strategy for lowering methane yield, but wool, live weight and fat deposition traits may be affected over time and should be monitored.