Over the history of the Earth, changes in ocean depth and coastal configuration have led to considerable variations in the pattern and amplitude of ocean tides. Here we perform global simulations of ocean tides for the Last Glacial Maximum, using new data sets for both ocean depth and density stratification. We show how the configuration of the Arctic Ocean, which was almost entirely enclosed by continents at that time, leads to the near-resonant excitation of large semi-diurnal tides. Under certain conditions, this previously unidentified Arctic tide is massively amplified in the Canadian Archipelago. Such tides may have played a role in destabilizing the coastal margins of North American ice sheets, with implications for rapid changes in the Earth's climate and ocean circulation.