Climate change will have serious effects on the planet and on its ecosystems. Currently, mitigation efforts are proving ineffectual in reducing anthropogenic CO2 emissions. Coral reefs are the most sensitive ecosystems on the planet to climate change, and here we review modelling a number of geoengineering options, and their potential influence on coral reefs. There are two categories of geoengineering, shortwave solar radiation management and longwave carbon dioxide removal. The first set of techniques only reduce some, but not all, effects of climate change, while possibly creating other problems. They also do not affect CO2 levels and therefore fail to address the wider effects of rising CO2, including ocean acidification, important for coral reefs. Solar radiation is important to coral growth and survival, and solar radiation management is not in general appropriate for this ecosystem. Longwave carbon dioxide removal techniques address the root cause of climate change, rising CO2 concentrations, they have relatively low uncertainties and risks. They are worthy of further research and potential implementation, particularly carbon capture and storage, biochar, and afforestation methods, alongside increased mitigation of atmospheric CO2 concentrations.