For the long gap tunable undulator systems of the European XFEL, 91 phase shifters are needed. They need to fulfil stringent and demanding field integral tolerances if their strengths, i.e., their magnetic gaps, are changed. In order to avoid additional correctors, their first field integral errors must not exceed ±0.004  Tmm for self-amplified spontaneous emission operation at 1 Å. For longer wavelengths there are slightly relaxed requirements. In addition, a good field range of ±0.5  mm is required. Phase shifters are manufactured by using state of the art techniques such as measurement and sorting of magnets, measurement and sorting of subassemblies, etc. In spite of these efforts, inhomogeneities of the permanent magnet material as well as mechanic manufacturing errors, which cannot be avoided and lead to violations of the demanding first field integral specifications. Therefore, a fast and robust shimming technique was developed for the serial production of these devices. It is based on measured signatures of shims with different geometries and uses symmetry properties of shims placed on different positions and poles with different polarity. In this paper, the specifications for the phase shifters in the European XFEL are derived first. Then the method is described in detail and results are presented, which demonstrate that all requirements can be fulfilled.