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This paper is a contribution to the development of microwave plasma-based technology aimed at efficient hydrogen (H2) production from a so-called synthetic biogas, considered a mixture of methane (CH4) and carbon dioxide (CO2), which can contain up to 70% CH4. In this work, we tested the performance of a waveguide-supplied metal cylinder-based microwave plasma source (MPS) operating at 915 MHz at atmospheric pressure as a tool for the efficient production of H2 in the steam reforming of the synthetic biogas. The test showed that the steam reforming of the synthetic biogas could be carried out under a wide range of working parameters without soot formation and extinction of the microwave discharge. We found that there is a minimal H2Osteam consumption rate for a given CH4 input volume content, which ensures stable operation of the MPS (no soot). The experiments did not show that increasing the amount of H2Osteam rate above the minimal value for a given CH4 input volume content results in an increase in the H2 production rate, energy yield, CH4 conversion degree, and H2 output concentration. To describe the MPS performance, which also takes into account a factor of the utilization of the CH4 feedstock, we introduced a new parameter, called an energy–CH4 feedstock consumption yield. The best results in terms of the H2 production rate, the energy yield, and the CH4 conversion degree were 239 g[H2]/h 36.8 g[H2]/kWh, and 74.3%, respectively. This shows that the application of the steam reforming, instead of the dry reforming, resulted in a 1.5-fold increase of the H2 production rate and the corresponding energy yield.