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Unlike anisotropy of magnetic susceptibility (AMS), which can be determined in a more or less simple way, the determination of anisotropy of magnetic remanence (AMR) is a relatively complex and laborious procedure involving a series of demagnetizations, directional magnetizations and measurements of the imparted directional remanence.This complexity may logically imply larger errors in subsequent fitting of the AMR tensors compared to the AMS. The accuracy of the AMR determination primarily depends on the precision of imparting the directional remanence, the number of measuring directions, and the symmetry of the measuring design. The importance of the above control factors was investigated by means of mathematical modelling.As shown in the previous model studies, the precision of the determination of the anisotropy of magnetic remanence (AMR) is directly proportional to the precision of the determination of the directional remanent magnetizations with respect to the degree of anisotropy. While the AMR imparted in weak to moderate fields is relatively commonly used in rock fabric studies (e.g., anisotropy of anhysteretic remanent magnetization), only a few attempts to determine the AMR in high fields (hfAMR) were reported most likely due to instrumental (insufficient precision in setting up the intensity of magnetizing field and its insufficiently homogeneity) or other methodological reasons.Recently, a high-field impulse magnetizer has been developed (commercial name PUMA) that allows the standard palaeomagnetic specimen to be magnetized in a set of 18 predefined directions in the wide range of magnetic fields ranging from 1 mT to 5 T.The elaborate design of this magnetizer allows precise setting of the pulse intensity and high homogeneity of the field over the entire specimen volume. To experimentally assess the precision of the hfAMR determination, the reproducibility in imparting the magnetic remanence in the same direction by the same magnetizing field was examined. We also investigated whether it was necessary to demagnetize the specimen between individual magnetizations to improve the remanence reproducibility despite the fact that each high field magnetization (“saturation”) should theoretically obliterate the previous remanence. The investigations were made on specimens having single mineral ferromagnetic fraction (magnetite, hematite, and pyrrhotite). The results helped us to decide whether the hfAMR is convenient to most rocks or only to strongly magnetic and strongly anisotropic ones.In order to fit the AMR tensors, we present a simple, user-friendly toolbox which facilitates tensor fitting from an array of magnetic remanence vectors according the chosen magnetizing design (6, 9, 12, 15, 18 directions). This toolbox provides a graphical visualization of the intensity of measured remanence vectors and their directional comparison with the respective magnetizing directions.