Beef cattle contribute 7% of anthropocentric greenhouse gas emissions in Australia through the release of methane into the atmosphere. Cattle in northern Australia produce more methane per unit of beef produced because tropical grasses are generally of poor quality and elicit slower average growth rates. In this paper the level of emissions from different herds and some strategies to reduce emissions are estimated with a daily time-step model. The results indicate that few options exist to reduce methane emissions from extensive grazing systems without reducing beef production. Options to improve production or feed conversion efficiencies can generate lower levels of emissions per kg of beef produced, but can be expected to lead to increased livestock numbers and higher overall methane emissions. A woodland grazing case study from central Queensland suggests the opportunity cost of reducing each kg of methane emissions by reducing stocking rates ranges from 1.0 to 1.2 kg of liveweight beef production. A price of $23 per t of carbon dioxide equivalent would indicate that opportunity costs (ignoring fixed costs of production) of reducing emissions by adjusting stocking rates would range between $0.39 and $0.49 per kg of beef produced.