The Geometric Product Specification (GPS) and Geometric Dimensioning and Tolerancing (GD&T) languages are the most powerful tools available for linking an ideal design to imperfectly manufactured parts that are never assembled with absolute accuracy. In the design of mechanical systems, the GPS and GD&T methods provide a symbolic language that allows for the complete, clear, and unambiguous definition of permissible variations from ideal geometries to ensure functionality and assemblability. This study proposes a methodology for assigning functional tolerances for the manufacture and assembly of hinges with pins supported by close-range bushings. A test machine was developed to measure the resistant torque in these types of hinges and an easy experimental procedure was used to measure and verify the cylindricity tolerance of the hinge bushings. This allowed a Design for Tolerancing (DfT) approach based on a correlation between the resistant torque values and dimensional and geometric errors. The proposed approach proved to be effective in establishing a relationship between shape, position and orientation errors and the functionality of the hinge. In the scientific literature on these systems, in fact, there are no correlations between the functionality of the hinge in terms of resistant torque and the dimensional and geometric tolerance values.