Existing vital sign monitoring systems in the neonatal intensive care unit (NICU) require multiple wires connected to rigid sensors with strongly adherent interfaces to the skin. We introduce a pair of ultrathin, soft, skin-like electronic devices whose coordinated, wireless operation reproduces the functionality of these traditional technologies but bypasses their intrinsic limitations. The enabling advances in engineering science include designs that support wireless, battery-free operation; real-time, in-sensor data analytics; time-synchronized, continuous data streaming; soft mechanics and gentle adhesive interfaces to the skin; and compatibility with visual inspection and with medical imaging techniques used in the NICU. Preliminary studies on neonates admitted to operating NICUs demonstrate performance comparable to the most advanced clinical-standard monitoring systems.