In a globalized marketplace, the competition in the aerospace industry has increased significantly. Producers can choose between many suppliers. These suppliers have to comply with more requirements and technical specifications, as well as take on greater responsibilities that originally fell on producers. In this context, business opportunities for small and medium-sized enterprises (SMEs) are limited, but still suppliers must try to leverage the maximum strategic advantage of the few that present. Adopting research, development and innovation (R+D+i) practices has proven to bring great benefits to companies and allows them to gain significant competitive advantages. However, the process of designing, implementing and testing R+D+i-related processes is not straightforward, nor it has been addressed in the recent research on SMEs. In this paper, a case study of a Spanish innovative small company providing industrial metrology and quality services is analyzed. Thanks to an internal decision-making process, an R+D+i management system based on the UNE 166.002:2014 standard is eventually adopted. A pilot project is closely followed up to test the robustness of the system implementation. The R+D+i management system has allowed the company to streamline its innovation activities, establish objectives to better allocate essential resources, organize high performing innovation units within the organization structure, increase the clients’ confidence, improve the company’s competitiveness, carry out technological surveillance, and get more patented technology, among many others. Adoption steps taken by this SME are generalizable to other SMEs from other industries and show how an R+D+i management system can be chosen, designed, implemented and tested in the context of Industry 4.0 (I4.0).