‘Climate change inundation’ – the process whereby climate change-related impacts like rising sea levels, higher storm surges, and changing rainfall patterns interact with and exacerbate existing vulnerabilities like poverty, isolation, resource scarcity, and inadequate infrastructure – presents a unique challenge to the territorial, legal, and political infrastructure of low-lying coral atoll island states. This article uses the example of climate change inundation to illustrate some of the shortcomings of the mainstream ‘minimum threshold’ account of statehood. It then proposes an alternative account of the criteria of statehood as a set of overlapping similarities or relationships between state-like entities, drawing on Wittgenstein's concept of ‘family resemblances’. Although problematic in some respects, this family resemblance account provides a broader conceptual space for assessing the merits of alternative forms of statehood.