This paper describes a technique for the position error estimations and compensations of the modeless robots and manipulators calibration process based on a shallow neural network fitting function method. Unlike traditional model-based robots calibrations, the modeless robots calibrations do not need to perform any modeling and identification processes. Only two processes, measurements and compensations, are necessary for this kind of robots calibrations. By using the shallow neural network fitting technique, the accuracy of the position error compensation can be greatly improved, which is confirmed by the simulation results given in this paper. Also the comparisons among the popular traditional interpolation methods, such as bilinear and fuzzy interpolations, and this shallow neural network technique, are made via simulation studies. The simulation results show that more accurate compensation result can be achieved using the shallow neural network fitting technique compared with the bilinear and fuzzy interpolation methods.