The behaviours of a swarm are not explicitly engineered. Instead, they are an emergent consequence of the interactions of individual agents with each other and their environment. This emergent functionality poses a challenge to safety assurance. The main contribution of this paper is a process for the safety assurance of emergent behaviour in autonomous robotic swarms called AERoS, following the guidance on the Assurance of Machine Learning for use in Autonomous Systems (AMLAS). We explore our proposed process using a case study centred on a robot swarm operating a public cloakroom.