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Biomaterials composed of synthetic cells have the potential to adapt and differentiate guided by physicochemical environmental cues. Inspired by biological systems in development, which extract positional information (PI) from morphogen gradients in the presence of uncertainties, we here investigate how well synthetic cells can determine their position within a multicellular structure. To calculate PI, we created and analyzed a large number of synthetic cellular assemblies composed of emulsion droplets connected via lipid bilayer membranes. These droplets contained cell-free feedback gene circuits that responded to gradients of a genetic inducer acting as a morphogen. PI is found to be limited by gene expression noise and affected by the temporal evolution of the morphogen gradient and the cell-free expression system itself. The generation of PI can be rationalized by computational modeling of the system. We scale our approach using three-dimensional printing and demonstrate morphogen-based differentiation in larger tissue-like assemblies.