Supramolecular synthesis is a powerful strategy for assembling complex molecules, but to do this by targeted design is challenging. This is because multicomponent assembly reactions have the potential to form a wide variety of products. High-throughput screening can explore a broad synthetic space, but this is inefficient and inelegant when applied blindly. Here we fuse computation with robotic synthesis to create a hybrid discovery workflow for discovering new organic cage molecules, and by extension, other supramolecular systems. A total of 78 precursor combinations were investigated by computation and experiment, leading to 33 cages that were formed cleanly in one-pot syntheses. Comparison of calculations with experimental outcomes across this broad library shows that computation has the power to focus experiments, for example by identifying linkers that are less likely to be reliable for cage formation. Screening also led to the unplanned discovery of a new cage topology—doubly bridged, triply interlocked cage catenanes.