Control over magnetism in single-walled carbon nanotubes (SWCNTs) and graphene is of fundamental importance. Creation and manipulation using the unpaired spins without the need for archetypal magnetic elements results in sp(2)-hybridised nanocarbons being at the forefront of applications in both spintronics and nanoelectronics. The crucial limitation for the experimental observation of the intrinsic carbon magnetism stems from the presence of magnetic impurities, from which a magnetic response usually dominates. Thus, the rigorous identification of such magnetic impurities and their efficient removal is of enormous importance. The present review reports on the current state-of-the-art methodology for the detection and quantification of magnetic impurities in SWCNTs and graphene, reflecting both the preparation and subsequent purification procedures. First, the most common techniques for the preparation of SWCNTs (i.e., arc discharge, laser ablation and chemical vapour deposition) and the corresponding magnetic impurities are reviewed. Then, the available volume, surface and local probes for the identification and quantification of the impurities are discussed, and their efficiency and limitations are evaluated for the given cases. A summary of the current understanding of graphene-related magnetism in the context of the identified impurities is also given. Finally, the key knowledge is reviewed with respect to future prospects in the field.