The majority of the projects funded under the European Research Framework Programme (FP) require a collaborative effort in order to tackle complex societal challenges. The underlying assumption is that collaborative networks boost research productivity and the attainment of the goals set out by the European Commission's agenda. In general, the production of scientific knowledge increasingly takes place within networks and consortia with a wide diversity and interlinkages of disciplines, expertise, backgrounds and approaches. This relational dimension has become even more important in the Horizon Europe FP, which has moved from a project-focused to a mission-oriented approach whereby a portfolio of projects is managed in coordination in order to stimulate cross-learning and experimentation. Starting from key concepts and theories of evaluation research, including ten years of experience for the Italian National Research Council (CNR) team as an internal evaluator, we are proposing a new approach, namely a Relations-based Evaluation (RE) approach, that analyses, assesses and builds relationships, both internal and external, with the ultimate aim of supporting collaborative research and innovation (R&I) projects. The framework originated within the context of EU projects and deals with the specific case of consortia funded under the EU FPs. However, it could be easily applied to other types of research consortia and project networks with similar features.