The remarkable mechanical performance of biominerals often relies on distinct crystallographic textures, which complicate the determination of the nanohardness from indentations with the standard non-rotational-symmetrical Berkovich punch. Due to the anisotropy of the biomineral to be probed, an azimuthal dependence of the hardness arises. This typically increases the standard deviation of the reported hardness values of biominerals and impedes comparison of hardness values across the literature and, as a result, across species. In this paper, we demonstrate that an azimuthally independent nanohardness determination can be achieved by using a conical indenter. It is also found that conical and Berkovich indentations yield slightly different hardness values because they result in different pile-up behaviors and because of technical limitations on the fabrication of perfectly equivalent geometries. For biogenic crystals, this deviation of hardness values between indenters is much lower than the azimuthal variation in non-rotational-symmetrical Berkovich indentations.