The use of soft X-rays near the carbon edge of absorption (270-300eV) greatly enhances studies in various branches of science. However, the choice of reflecting coatings for mirrors operating in free-electron and X-ray free-electron laser (FEL and XFEL) beamlines in this spectral range is not so evident and experimental justifications of the mirror efficiency are rather limited. In the present paper it is demonstrated experimentally that the reflectivity of B4C- and Ni-coated grazing-incidence mirrors is high enough for their operation in FEL or XFEL beamlines near the carbon K-edge of absorption. The minimal reflectivity of both mirrors proves to exceed 80% near the carbon absorption edge at a grazing angle of 0.6-. An in-depth profile of the chemical elements composing the reflecting coatings is reconstructed based on analysis of a set of reflectivity curves measured versus the grazing angle at different photon energies in the soft X-ray spectral region. This allows us to predict correctly the mirror reflectivity at any X-ray energy and any grazing angle.