Out-of-school science education institutions, such as museums, science centres, zoos and aquaria, have strong potentials to promote sustainability, yet seem to lack an operational definition of sustainability that aligns with their specific characteristics and institutional remit. Here, we use the anthropological theory of didactics to systematically develop such an operational definition, designated as the reference model. We draw on literature from research and practice to account for the features of sustainability science and policy, as well as the different specific strengths of out-of-school science education institutions, to identify unique potentials for sustainability education. These potentials are synthesised and illustrated in a set of institutionally specific guidelines that optimise the organisation of sustainability for each kind of out-of-school science education institution. We conclude by considering the implications of our findings for sustainability education.