This paper introduces a novel Multi-Criteria Decision Analysis (MCDA) framework for systematic evaluation and alignment of business models for community microgrids within local energy markets (LEMs). Our approach uniquely integrates social capital as a critical metric for assessing the success of these models. The framework's robustness is demonstrated through a case study application, showcasing its utility as a decision-support tool. This tool effectively bridges the gap between the operational and technical aspects of microgrids with the socio-economic context of the communities they serve. A key contribution is the establishment of a systematic categorisation of business models and LEMs facilitated by the MCDA framework. This approach emphasises the importance of analysing the synergy between business model components (ownership, revenue/pricing, activities, value proposition) and the corresponding market mechanisms, infrastructure, and ICT frameworks. The results demonstrate how the framework guides an informed and context-sensitive selection of business models, leveraging the interconnected socio-technical dynamics inherent to community energy systems.