Masonry vaults are widespread in the ancient built environment; they frequently provide a load-bearing purpose and can have numerous variables that influence structural behaviour, e.g., shape, materials, and boundary conditions. These structures may require strengthening interventions to increase load-bearing capacity and minimise vulnerability. In the presence of masonry substrate, intervention approaches based on inorganic matrix composite materials are preferred. Despite their growing popularity, there are just a few experimental campaigns in the literature that employ these composite materials to reinforce curved surfaces. The current study intends to contribute to this field by investigating the behaviour of barrel vaults composed of calcarenite stone masonry reinforced with Composite Reinforced Mortar (CRM). Specifically, the preliminary outcomes of the proposed experimental program will be presented. Simultaneously, a Finite Element (FE) model was calibrated in order to interpret the data and gain a better understand the phenomenology. The results obtained can provide useful hints for the design of this strengthening intervention.