•Lab and field bond tests are carried out on SRG applied to convex masonry substrates.•SRG-to-substrate bond behaviour is improved by compressive normal stresses induced by curvature.•Bond strength increases with the increase of substrate curvature and bond length.•Cord-to-matrix interlocking is crucial for the effectiveness of the reinforcement.•Bond behaviour is independent from the mechanical properties of the vault substrate. Steel Reinforced Grout (SRG), consisting of ultra high tensile strength steel cords embedded in a mortar matrix, is an effective solution for the upgrade of existing structures. Among its various applications, it can be applied to the extrados and the intrados of masonry vaults to improve their load-carrying and seismic capacity. Nevertheless, its bond strength on curved substrates, which is crucial for the design of the reinforcement of masonry arched members, has not been properly explored yet. This paper presents an experimental investigation on the bond behaviour of SRG applied to convex masonry substrates. Double-lap shear bond tests were carried in the laboratory on small-scale brickwork specimens to investigate the effect of curvature radius, bond length and textile architecture on bond strength and failure mode. Full-scale field tests were performed to study the bond behaviour and the resisting mechanisms of SRG applied to the extrados of an existing masonry vault, taking into account the actual substrate preparation and mortar curing conditions at a construction site.