Organ chips can recapitulate organ-level (patho)physiology, yet pharmacokinetic and pharmacodynamic analyses require multi-organ systems linked by vascular perfusion. Here, we describe an 'interrogator' that employs liquid-handling robotics, custom software and an integrated mobile microscope for the automated culture, perfusion, medium addition, fluidic linking, sample collection and in situ microscopy imaging of up to ten organ chips inside a standard tissue-culture incubator. The robotic interrogator maintained the viability and organ-specific functions of eight vascularized, two-channel organ chips (intestine, liver, kidney, heart, lung, skin, blood-brain barrier and brain) for 3 weeks in culture when intermittently fluidically coupled via a common blood substitute through their reservoirs of medium and endothelium-lined vascular channels. We used the robotic interrogator and a physiological multicompartmental reduced-order model of the experimental system to quantitatively predict the distribution of an inulin tracer perfused through the multi-organ human-body-on-chips. The automated culture system enables the imaging of cells in the organ chips and the repeated sampling of both the vascular and interstitial compartments without compromising fluidic coupling.