Conventional current transformers (CTs) suffer from nonlinearities due to their ferromagnetic cores. On one hand, it is well-known that severe core saturation may occur because of large overcurrents or unidirectional transient components: this may substantially impact the operation of relays. On the other hand, weaker nonlinear effects are also present during regular working conditions. In particular, the spectral content of typical current waveforms is characterized by a strong fundamental term responsible for harmonic distortion affecting the frequency components at the secondary side. In turn, this has a significant impact on the accuracy that can be reached as long as current harmonics must be monitored. The target of this work is implementing a simple signal processing technique that allows compensating for this effect. The method, characterized by extremely low computational complexity, is first introduced and validated using numerical simulations. After this, it was tested experimentally to improve the harmonic measurement capability of inductive CTs. The achieved results highlight a noticeable reduction of errors at low-order harmonics over a wide range of primary current amplitudes. It is worth noting that the black-box approach makes the technique suitable also for compensating nonlinearities introduced by current transducers based on different operating principles. Thanks to this peculiarity and to the low computational complexity, the proposed method is suitable to be employed in power quality analyzers and merging units. In this way, high-accuracy monitoring of current harmonics in power systems can be achieved, opening the way to advanced power quality management and to the location of disturbing users.