<p><b>Context:</b> Cattle and sheep emit methane, a potent greenhouse gas, as part of the fermentation process of feed digestion in their gut; however, the mechanisms explaining differences among animals in enteric methane production are not fully understood. <b>Aim:</b> To investigate whether variation among animals in their ability to digest their test ration was associated with phenotypic and genetic variation in methane production. <b>Methods:</b> The experiment used 135 Angus beef cattle measured for their phenotypic and genetic merit for methane production. The extent of digestion of the dry matter (DMD) in the test ration by individual cattle was determined using silica as a naturally present indigestible marker. Its concentration in feed consumed and faeces was determined using rapid portable X-ray fluorescence spectroscopy, from which DMD was calculated. <b>Key results:</b> Higher daily methane-production rate (MPR), higher methane produced per unit of feed consumed (methane yield; MY) and higher methane produced than the predicted daily production (residual MPR; RMP) by animals was accompanied by higher DMD. Higher genetic merit for MPR was also accompanied by higher DMD, but DMD had no detectable association with genetic variation in the other two methane emission traits. The regression coefficients for change in MPR (g/day), MY (g/kg DMI), RMP (g/day) with change in DMD (%) were 2.6 ± 1.1 (s.e.; P < 0.05), 0.14 ± 0.07 (P < 0.1) and 0.68 ± 0.38 (P < 0.1) respectively. <b>Conclusions:</b> Differences among animals in their DMD were found and were associated with phenotypic variation in the three methane emission traits studied, and with genetic variation in daily methane production. The results support the caution that feeding and breeding interventions seeking to reduce methane emissions can also reduce the extent of digestion of feed by cattle. <b>Implications:</b> Feeding and breeding interventions that seek to reduce methane emissions may change rumen physiology and reduce the extent of digestion of feed by cattle, which may be undesirable.</p>