Lead projectiles (non-ferromagnetic) are common foreign bodies in the medical practice. Conventional means of location use ionizing radiation, pose health risks and lead to procedures that last several hours, typically ending unsuccessfully. Magnetic field maps obtained non-invasively and innocuously with SQUIDs benefit the location of ferromagnetic metallic needles, reducing the time of successful removal from 6 hours to 10 minutes. SQUIDs are currently the most sensitive magnetometers, however require cryogenic temperatures, leading to high cost and low portability which prevent widespread clinical use. The objective is to design a device for locating non-ferromagnetic metallic foreign bodies for surgical removal, respecting project requirements of: high sensitivity, innocuousness, non-invasiveness, low cost, safety, portability, ease of use and room temperature operation. GMR and GMI sensors are considered as more suitable alternatives. Classical electrodynamics theoretical models applied to eddy currents induction serve as framework. Two electronic location systems are developed in gradiometric configuration to remove environmental interference, using commercially available GMR and GMI sensor elements. System performance is obtained from simulation results, demonstrating the capability of detecting the magnetic flux density levels expected under certain projectile radii and distances. The GMI system is more qualified, as its higher sensitivity and improved resolution favors larger measurement ranges, innocuousness, safety and ease of use. The results prove the viability of using GMI sensor elements in this application. The benefits of lower cost, higher portability and safety facilitate the clinical use of more innocuous and effective location techniques for non-ferromagnetic metallic foreign bodies.