Islands can offer safe refuge for vulnerable native species, so New Zealand is fortunate to have >250 islands managed as reserves. Stoats can swim for at least 2 h non-stop at steady 1 km/h, potentially longer if assisted by a current or a floating log. Stoats have got onto some 100 islands, but have never reached the most important ones. Stoats have been eradicated from 15 islands of >100 ha, and those located >5 km from shore are usually safe. Resolution and Secretary Islands are rugged enough to make trapping expensive and difficult, and both are well within swimming range of stoats. Stoats resident on Resolution island breed fast and avoid traps, but can be suppressed enough to allow some reintroductions of native species. Mop-up operations with toxins cannot be used where native species are at risk. Any incursion on a stoat-free island already repopulated by sensitive native fauna demands an immediate and expensive emergency response. Intense genetic monitoring of stoats on Waiheke Island since 2016 continuously follows the movements and effective trap avoidance behaviour of stoats resident there. New Zealand experience is being applied to eradication of stoats on the UK Orkney Islands.