Robust manipulation and insertion of small parts can be challenging because of the small tolerances typically involved. The key to robust control of these kinds of manipulation interactions is accurate tracking and control of the parts involved. Typically, this is accomplished using visual servoing or force-based control. However, these approaches have drawbacks. Instead, we propose a new approach that uses tactile sensing to accurately localize the pose of a part grasped in the robot hand. Using a feature-based matching technique in conjunction with a newly developed tactile sensing technology known as GelSight that has much higher resolution than competing methods, we synthesize high-resolution height maps of object surfaces. As a result of these high-resolution tactile maps, we are able to localize small parts held in a robot hand very accurately. We quantify localization accuracy in benchtop experiments and experimentally demonstrate the practicality of the approach in the context of a small parts insertion problem.