Made from organic waste, biomethane is a source of renewable energy with reduced emission of greenhouse gases, that could replace fossil fuels in transportation, heating, and electricity production. Liquefaction of biomethane is necessary to reduce its volume and facilitate its transport from the production site to the site of use. The liquefaction processes suffer from low efficiency operating with less than a third of the Carnot coefficient of performance. This paper study and compare the performance of different potential refrigeration processes, to select the best candidate for the liquefaction of biomethane. All possible liquefaction processes were examined and two potential processes have been selected and modelled. The non-integrated cascade operating with pure refrigerants and the integrated cascade operating with mixed refrigerants were thermodynamically investigated and optimised. The results show that the non-integrated pure refrigerant cascade has a COP of 0.411, approximately twice as high as the integrated mixed refrigerant cascade which had a COP of 0.191. Consequently, it was selected as the best candidate for micro-scale biomethane liquefaction. This study highlights a new refrigeration cycle for the liquefaction of biomethane.