This article explores how judicial approaches to science relate to the procedural legitimacy of rulings in cases where the plaintiffs seek a change in a government's overall climate policy. It reviews challenges in court interaction with climate science and compares two prominent cases: Urgenda v. The State of the Netherlands and Neubauer et al. v. Germany. The selected lawsuits yield comparative interest in aiming for changes in national climate policies and emission mitigation targets, involving the same kind of evidence (Assessment Reports by the Intergovernmental Panel on Climate Change) but resulting in partially opposing decisions. The analysis reveals that scientific inputs informed courts about climate change risks and mitigation measures. It also suggests that differing approaches to scientific reports influenced contrasting decisions regarding mitigation targets. Finally, it provides insights into how engagement with evidence might impact judgments' legitimacy from a procedural perspective.