Although superresolution has been studied to huge impact in visual imaging, it is relatively unexplored in tactile robotics. Here we demonstrate a novel optical sensor design (the TacTip) capable of achieving 40-fold localization superresolution to 0.1mm accuracy compared with a 4mm resolution between tactile elements. This superresolution is reached for localizing a 40mm diameter hemicylinder with a tactile finger pad also of 40mm diameter. Deformations of the sensor surface are measured as displacements of molded internal pins, with pin separation thus defining sensor resolution. Active Bayesian perception for classifying object location was used to ensure robust localization and hence the magnitude of the superresolution. These results are comparable with those for capacitive tactile sensors, which we interpret as originating from a convergence in the taxel-based design of the optical sensor and capacitive tactile sensors. The attained superresolution is comparable to the best perceptual hyperacuity in humans.