Cities are at the forefront of the battle against climate change, but their efforts to reduce emissions and adapt to its consequences depend on the knowledge that informs policy decisions. Science policy interfaces (SPIs) are institutions that aim to connect science and other knowledge with policy, but how to ensure their legitimacy is still controversial and under-analyzed. In this empirical paper, informed by interviews, document analysis and stakeholder workshops, we build upon a theoretical framework to evaluate the legitimacy of SPIs in the context of urban transformations for climate change mitigation and adaptation. By analyzing the climate action plans of four cities from different regions of the world - Accra (Ghana), Bonn (Germany), Sao Paulo (Brazil), and Ahmedabad (India) - we demonstrate the importance of evaluating SPIs based on their legitimacy and identify criteria for doing so. Our findings provide practical insights into how SPIs can effectively connect knowledge with policy to promote sustainability and combat climate change. Overall, this paper highlights the critical role of SPIs in addressing the knowledge gap and advancing sustainability science, making it an important contribution to the field for both scientists and practitioners.