Ultra-lean methane combustion in porous burners is investigated by means of a pilot-scale demonstration of the technology supported by a computational fluid dynamics (CFD) modelling study. The suitability of porous burners as a lean-burn technology for the mitigation of methane emissions is also evaluated. Methane constitutes 14.3% of total global anthropogenic greenhouse gas emissions. The mitigation of these emissions could have a significant near-term effect on slowing global warming, and recovering and burning the methane would allow a wasted energy resource to be exploited. The typically low and fluctuating energy content of the emission streams makes combustion difficult; however porous burners—an advanced combustion technology capable of burning low-calorific value fuels below the conventional flammability limit—are a possible mitigation solution. A pilot-scale porous burner is designed expressly for the purpose of ultra-lean methane combustion. The burner comprises a cylindrical combustion chamber filled with a porous bed of alumina saddles, combined with an arrangement of heat exchanger tubes for preheating the incoming methane/air mixture. A CFD model is developed to aid in the design process. Results illustrating the operating range and behaviour of the burner are presented. Running on natural gas, the stable lean flammability limit of the system is 2.3 vol%, a considerable extension of the conventional lean limit of 4.3 vol%; operating in the transient combustion regime allows the lean limit to be reduced further still, to 1.1 vol%. The heat exchanger arrangement is found to be effective; preheat temperatures of up to 800K are recorded. Emissions of carbon monoxide and unburned hydrocarbons are negligible. The process appears stable to fluctuations in fuel concentration and flow rate, typically taking several hours to react to any changes. A CFD model of the porous burner is developed based on the commercial CFD code ANSYS CFX 12.0. The burner is modelled as a single 1-dimensional porous domain. Pressure loss due to the presence of the porous solid is accounted for using an isotropic loss model. Separate energy equations for the gas and solid phases are applied. Models for conductive heat transfer within the solid phase, and for convective heat transport between the gas and solid phases, are added. Combustion is modelled using a finite rate chemistry model; a skeletal mechanism for ultra-lean methane combustion is developed and incorporated into the model to describe the combustion reaction. Results from the model are presented and validated against experimental data; the model correctly predicts the main features of burner behaviour. Porous burners are found to show potential as a methane mitigation technology.