As the use of artificial intelligence (AI) in high-stakes decision-making increases, the ability to contest such decisions is being recognised in AI ethics guidelines as an important safeguard for individuals. Yet, there is little guidance on how AI systems can be designed to support contestation. In this paper we explain that the design of a contestation process is important due to its impact on perceptions of fairness and satisfaction. We also consider design challenges, including a lack of transparency as well as the numerous design options that decision-making entities will be faced with. We argue for a human-centred approach to designing for contestability to ensure that the needs of decision subjects, and the community, are met.