In this paper we compare three approaches to solve the hand-eye and robot-world calibration problem, for their application to a Transcranial Magnetic Stimulation (TMS) system. The selected approaches are: i) non-orthogonal approach (QR24); ii) stochastic global optimization (SGO); iii) quaternion-based (QUAT) method. Performance were evaluated in term of translation and rotation errors, and computational time. The experimental setup is composed of a 7 dof Panda robot (by Franka Emika GmbH) and a Polaris Vicra camera (by Northern Digital Inc) combined with the SofTaxic Optic software (by E.M.S. srl). The method resulted to have the best performance, since it provides lowest errors and high stability over different datasets and number of calibration points. The only drawback is its computational time, which is higher than the other two, but this parameter is not relevant for TMS application. Over the different dataset used in our tests, the small workspace (sphere with radius of 0.05) and a number of calibration points around 150 allow to achieve the best performance with the method, with an average error of 0.83 ± 0.35 for position and 0.22 ± 0.12 for orientation.