After a decade of efforts to mainstream Responsible Research and Innovation (RRI) across Europe, the policy momentum is now uncertain. We explore how 217 organisations perceive responsibility in relation to their work, what mechanisms they apply to promote responsible practices, and what hindrances to promoting RRI they observe. Most organisations are unfamiliar with RRI but employ diverse perceptions of responsibility and mechanisms to promote it nonetheless. Civil society organisations are primarily outward oriented; collaborating with others and hosting science events. Private companies are more internally focussed and more likely to formalise this effort in strategies and internal guidelines. Universities resemble private companies, while private and public funders use funding-specific tools to incentivise responsible practices. Our results suggest that RRI is still poorly institutionalised and that some areas lack attention among actors in the research and innovation systems. Future policy endeavours might benefit from addressing deficits and tapping into existing perceptions of responsibility.