Geographical phenomena impacting the shape of coastlines may have implications for the stability of maritime boundaries delimited by agreement or judicial process. Sea level rise resulting from human-caused climate change has recently arisen as an additional phenomenon compelling the re-assessment of the stability of maritime boundaries over time. In a recent article published in this Journal, Dr. Snjólaug Árnadóttir has argued that a solution to the challenges of coastline change could be for maritime boundaries to fluctuate following the fluctuation of the baselines on which their course depends. By way of reply to Dr. Árnadóttir’s suggestion, this article argues that fluctuating boundaries have no legal basis either in the United Nations Convention on the Law of the Sea or in judicial decisions. Moreover, the delimitation process in three stages, commonly applied by international courts and tribunals since the Black Sea judgment, appears to be ill-suited for establishing fluctuating boundaries. There seems to be other solutions to the problem of coastline change, which this article also briefly explores.