Linear climate mitigation models look into aggregated economic sectors and model greenhouse gas (GHG) emissions disregarding downstream value chains, making particular sectors accountable for downstream (or upstream) GHG emissions. Hence, the present climate mitigation models inconsistently account for indirect GHG emissions; underrepresent upstream and downstream value chains; do not address Circular Economy (CE) practices; do not cover resource consumption, thus not considering materials’ circularity. To provide curated policy support for decision-making for carbon neutrality and other Sustainable Development Goals (SDGs), models need to shift from linear to circular. To achieve this, a link between energy-climate mitigation modelling and cradle-to-cradle assessment CE analytical tools must be established. This is the core issue covered in the CO2NSTRUCT Horizon project (2022-2026). CO2NSTRUCT proposes a framework to supplement the well-established JRC-EU-TIMES model, using a highly comprehensive technological representation with CE measures. The framework will apply CE measures to the value chain of six carbon-intensive construction materials (i.e., cement, steel, brick, glass, wood, and insulation materials) and will provide new components to the JRC-EU-TIMES model, including citizen behaviour; societal impacts; rebound effects; supply and value chains. The results will be used for policy approaches integrating CE into climate change mitigation actions.