Continuous cardiac monitoring using electrocardiograms (ECG) provides a range of patient information, essential for making clinical decisions, to healthcare providers. Unfortunately, the clinical standard of ECG recording requires the use of rigid metal electrodes, conductive gels, and wired electronic devices, which often cause skin injuries and health risks for pediatric patients with underdeveloped, fragile skin. Here, we introduce a wireless, soft, comfortable electronic system that obviates the need for skin preparation, electrolyte gels, or aggressive tapes. The low-profile device incorporates a thin-film circuit and nanomembrane sensors, encapsulated in a hyperelastic elastomer. The soft elastomeric membrane offers an optimized adhesion that ensures a conformal lamination of stretchable electrodes on the skin for recording of high-fidelity biopotentials. The combined set of on-board Bluetooth module, front-end amplifier, and voltage regulator enables a real-time, long-range, wireless monitoring of physiological data, including ECG, heart rate (HR) and respiratory rate (RR). A pilot study with pediatric patients demonstrates the clinical feasibility of the device as a comfortable, reliable biopotential monitor, suggesting a new standard for safe and effective pediatric care.