The recent narrative on museums as catalysts of innovation and growth considers their relations with other cultural and creative industries (CCIs) to be very important. We argue that most relations museums establish with CCI firms and institutions are unlikely to produce strong positive externalities that make the latter more innovative. To prove this claim, we propose a conceptual framework qualifying project-based and supply chain relations between museums and CCIs as either strong, moderate, or weak links, according to their potential in terms of knowledge spillovers from museums to CCIs. We apply this taxonomy to data collected from 261 Polish museums. Our findings indicate that strong links are outnumbered by moderate and weak ones. We then suggest that the traditional missions of museums, in particular education and conservation, need to be more thoroughly assessed in terms of their direct and indirect contributions in order to fully capture the impact of museums on innovation in the wider economy.