Positioning is considered one of the key features in various novel industry verticals in future radio systems. Since path loss (PL) or received signal strength-based measurements are widely available in the majority of wireless standards, PL-based positioning has an important role among positioning technologies. Conventionally, PL-based positioning has two phases—fitting a PL model to training data and positioning based on the link distance estimates. However, in both phases, the maximum measurable PL is limited by measurement noise. Such immeasurable samples are called censored PL data and such noisy data are commonly neglected in both the model fitting and in the positioning phase. In the case of censored PL, the loss is known to be above a known threshold level and that information can be used in model fitting and in the positioning phase. In this paper, we examine and propose how to use censored PL data in PL model-based positioning. Additionally, we demonstrate with several simulations the potential of the proposed approach for considerable improvements in positioning accuracy (23–57%) and improved robustness against PL model fitting errors.