Mounting evidence that even aggressive reductions in net emissions of greenhouse gases will be insufficient to limit global climate risks is increasing calls for atmospheric experiments to better understand the risks and implications of also deploying solar geoengineering technologies to reflect sunlight and rapidly lower surface temperatures. But solar geoengineering research itself poses significant environmental and geopolitical risks. Given limited societal awareness and public dialogue about this climate response option, conducting such experiments without meaningful societal engagement could galvanize opposition to solar geoengineering research from civil society, including the most climate vulnerable communities who are among its intended beneficiaries. Here, we explore whether and how a solar geoengineering research enterprise might be developed in a way that promotes legitimacy as well as scientific credibility and policy relevance. We highlight the distinctive responsibilities of researchers and research funders to ensure that solar geoengineering research proposals are subject to legitimate societal review and scrutiny, recommend steps they can take to strive towards legitimacy and call on them to be explicitly open to multiple potential outcomes, including the societal rejection or considerable alteration of the solar geoengineering research enterprise. 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'.