The continuous monitoring of arterial blood pressure (BP) is vital for assessing and treating cardiovascular instability in a sick infant. Currently, invasive catheters are inserted into an artery to monitor critically-ill infants. Catheterization requires skill, is time consuming, prone to complications, and often painful. Herein, we report on the feasibility and accuracy of a non-invasive, wearable device that is easy to place and operate and continuously monitors BP without the need for external calibration. The device uses capacitive sensors to acquire pulse waveform measurements from the wrist and/or foot of preterm and term infants. Systolic, diastolic, and mean arterial pressures are inferred from the recorded pulse waveform data using algorithms trained using artificial neural network (ANN) techniques. The sensor-derived, continuous, non-invasive BP data were compared with corresponding invasive arterial line (IAL) data from 81 infants with a wide variety of pathologies to conclude that inferred BP values meet FDA-level accuracy requirements for these critically ill, yet normotensive term and preterm infants.