Stem-cell-derived epithelial organoids are routinely used for the biological and biomedical modelling of tissues. However, the complexity, lack of standardization and quality control of stem cell culture in solid extracellular matrices hampers the routine use of the organoids at the industrial scale. Here, we report the fabrication of microengineered cell culture devices and scalable and automated methods for suspension culture and real-time analysis of thousands of individual gastrointestinal organoids trapped in microcavity arrays within a polymer-hydrogel substrate. The absence of a solid matrix substantially reduces organoid heterogeneity, which we show for mouse and human gastrointestinal organoids. We use the devices to screen for anticancer drug candidates with patient-derived colorectal cancer organoids, and apply high-content image-based phenotypic analyses to reveal insights into mechanisms of drug action. The scalable organoid-culture technology should facilitate the use of organoids in drug development and diagnostics.