The effectiveness of stringent climate stabilization scenarios for coastal areas in terms of reduction of impacts/adaptation needs and wider policy implications has received little attention. Here we use the Warming Acidification and Sea Level Projector Earth systems model to calculate large ensembles of global sea-level rise (SLR) and ocean pH projections to 2300 for 1.5°C and 2.0°C stabilization scenarios, and a reference unmitigated RCP8.5 scenario. The potential consequences of these projections are then considered for global coastal flooding, small islands, deltas, coastal cities and coastal ecology. Under both stabilization scenarios, global mean ocean pH (and temperature) stabilize within a century. This implies significant ecosystem impacts are avoided, but detailed quantification is lacking, reflecting scientific uncertainty. By contrast, SLR is only slowed and continues to 2300 (and beyond). Hence, while coastal impacts due to SLR are reduced significantly by climate stabilization, especially after 2100, potential impacts continue to grow for centuries. SLR in 2300 under both stabilization scenarios exceeds unmitigated SLR in 2100. Therefore, adaptation remains essential in densely populated and economically important coastal areas under climate stabilization. Given the multiple adaptation steps that this will require, an adaptation pathways approach has merits for coastal areas. This article is part of the theme issue ‘The Paris Agreement: understanding the physical and social challenges for a warming world of 1.5°C above pre-industrial levels’.