The functioning and the achievable power of a proton exchange membrane fuel cell (PEMFC) are determined by several parameters simultaneously. Part of these cannot be measured directly. They must be estimated with parameter fitting techniques. In order to give reliable estimations for the unknown parameters, we first set up an adequate finite difference numerical solution of the mathematical model of the fuel cell. Then the values of the unknown parameters are calculated by fitting the model results to measurements. In this paper our primary aim is to compare several parameter fitting tools on the model of a PEMFC and give a prescription for the use of these methods. We test three methods together with their variants: the Levenberg–Marquardt method, the trust region method, and the simulated annealing method, among which the Levenberg–Marquardt method turns to be the most efficient one.