Contact connections in electrical machines and apparatus are important elements in the whole power supply network and a high level of reliability is expected there. Contact resistance is a fundamental criterion in the design of an electrical contact or contact system. The contact resistance should be as low as possible to minimize losses due to the current passage and the related heating of the contact connection. The value of the contact resistance depends on the material used, the value of the applied force, the type of contact, and, last but not least, the quality of the surface and chemical layers. In this paper, an initial diagnosis of the contact material is performed based on the determination of the sample’s specific resistivity by the four-wire method and the evaluation of the measurement uncertainty. The work is followed by the design of a testing device that uses crossed bars to measure the change in contact resistance as a function of the magnitude of the applied force. An analysis of the sample mounting method is performed here using FEM simulations of the current field and shows the interaction between the holder and the sample in terms of current line transfer. The proposed system is then used for experimental measurements of the material-dependent coefficient KC for verification of existing or newly developed materials in electrical engineering, where the values of the KC coefficient are not known. Finally, the paper also deals with the measurement of fritting voltage for individual contact pairs having surface quality corresponding to brushing.