The heterogeneous and homogeneous combustion-based homogeneous charge compression ignition of fuel-lean methane-air mixtures over alumina-supported platinum catalysts was investigated experimentally and numerically in free-piston micro-engines without ignition sources. Single-shot experiments were carried out in the purely homogeneous and coupled heterogeneous and homogeneous combustion modes, involved temperature measurements, capturing the visible combustion image sequences, exhaust gas analysis, and the physicochemical characterization of catalysts. Simulations were performed with a two-dimensional transient model that includes detailed heterogeneous and homogeneous chemistry and transport, leakage, and free-piston motion to gain physical insight and to explore the heterogeneous and homogeneous combustion characteristics. The micro-engine performance concerning combustion efficiency, mass loss, energy density, and free-piston dynamics was investigated. The results reveal that heterogeneous reactions cause earlier ignition, which is very favourable for the micro-device. Both purely homogeneous and coupled heterogeneous and homogeneous combustion of methane-air mixtures in a narrow cylinder with a diameter of 3 mm and a height of approximately 0.3 mm are possible. Heat losses result in higher mass losses. The coupled heterogeneous and homogeneous mode can not only significantly improve the combustion efficiency, in-cylinder temperature and pressure, output power and energy density, but also reduce the mass loss because of its lower compression ratio and less time spent around the top dead centre and during the expansion stroke, indicating that this coupled mode is a promising combustion scheme for micro-engines.