Combined sewer overflows (CSOs), the discharge of untreated sewage mixed with stormwater into surface waters, are expected to increase under climate change as a result of more extreme rainfall. Blue-green infrastructure (BGI), such as bioretention cells and porous pavements, can help to reduce the amount of stormwater entering combined sewer systems, thus reducing CSO discharge. However, our understanding of the potential for BGI to mitigate CSOs in a future climate is still lacking, as performance is typically evaluated for individual BGI elements with fixed implementation areas under historical climate conditions or limited future scenarios. In response, this study investigates the performance of 30 combinations of BGI elements and implementation rates to prevent increases in CSOs under a range of future climate scenarios in an urban catchment near Zurich, Switzerland. Median total annual rainfall, projected to increase by as much as 46%, could double the median annual CSO volume and increase median annual CSO frequency by up to 52%. Four BGI combinations that include bioretention cells show the most promise to prevent increases in CSO volume and frequency in a future climate; and given the diverse responses of BGI elements to distinct rainfall patterns, their combinations can enhance CSO discharge reduction across varying climate patterns. BGI is also likely to become more cost-effective under future climatic conditions as projected increases in total rainfall led to larger CSO volume reductions obtained through BGI. However, there is a trade-off between robustness to climate change and cost-effectiveness, since CSO volume reduction capacity scales with BGI implementation rate but cost-effectiveness declines. Our study illustrates the effectiveness of various BGI combinations to prevent increases in CSOs in a future climate, calling for a range of BGI elements and implementation areas to be considered for urban drainage adaptation.