[EN]A systematic approach is developed for the conceptual optimal design of biomethane production via carbon capture. A hybrid heuristic-mathematical procedure is proposed to determine the optimal technology and operating conditions. The heuristic step consists of a literature-based screening of the available technologies. After the prescreening stage, the technologies selected are amine absorption, pressure swing adsorption (PSA), and membrane separation. The mathematical stage is composed of two steps. First, different alternatives for each technology are modeled based on first principles and rules of thumb. These models are used to select the optimal configuration for each process considered. Second, a superstructure model for biomethane production is developed integrating the pre-selected upgrading technologies to select the optimal process, as well as to determine the optimal operating conditions. Four waste sources are analyzed: cattle manure, swine manure, municipal food waste, and sludge. The results suggest that the best amine is diethanolamine (DEA), the best membrane material is the polyimide, and the suggested zeolite is 13X among the ones studied. Finally, among the three technologies, the overall results show that carbon capture using a PSA system using zeolite 13X results in lower production and investment costs, but very close to the use of membranes. The results indicate that food waste shows the lowest production cost for biomethane 0.36 €/Nm3, due to the largest organic matter content, whereas the investment costs are 67 M€, considering a biogas production rate of 0.035 kg of biomethane per kg of waste and the processing of 311 kt/yr of food waste. Credits or incentives are still needed for biomethane to be competitive with fossil natural gas. Junta de Castilla y León y USAL