Fuelling micro-combined heat and power (micro-CHP) devices using renewable sources, such as biogas, can enhance the energy and environmental benefits associated with such devices. This paper presents a solution for increasing the electric efficiency of biogas-fed Stirling co-generators by recuperating the energy content of the combustion flue gas. When economically and energetically convenient for micro-CHP operation, the exhausts can be used to pre-heat fresh combustion air. It was assessed that, due to the introduction of a spiral gas-gas heat exchanger, whose main design parameters were identified, the electric efficiency of the Stirling unit can be raised to up to 22.5%. To determine the advantages of applying the system analysed over a traditional Stirling device, a specific algorithm for the optimal management of the micro-CHP unit was built and applied to a residential case study. The results demonstrate that the extra cost of the high-efficiency recuperator can be easily recovered in approximately two years of system operation, providing an additional advantage over a standard Stirling device in terms of primary energy consumption and an approximately 6% increase in economic savings.