Owing to its system independence and unmatched speed, Traveling-wave (TW)-based relaying has become a top contender for transmission and distribution systems. However, existing measurement devices, such as Current Transformers (CTs), are incapable of capturing the full frequency content of TWs, as their bandwidths are limited. Consequently, existing TW-based schemes rely on distorted waveforms and partial-frequency spectra, i.e., low-frequency content, of TWs to perform protection tasks. Such incomplete information can lead to misoperation of protection schemes. This article investigates the impacts of the limited bandwidth of CTs on the shape and frequency content of TWs under faults in transmission and distribution lines. Additionally, it proposes a compensation technique, which utilizes an Unknown Input Kalman Filter (UIKF), to accurately estimate the primary current of a CT from the measured secondary one, i.e., to capture the waveshape and full frequency-content of TWs. The proposed method removes the bandwidth barrier from the measurement of current-TWs, and thus allows relays to access the High-Frequency (HF) spectra of TWs in order to devise more-effective TW-based schemes. Simulation results corroborate that the proposed method accurately compensates for low frequency-content and distorted waveform of TWs in the secondary currents of CTs under various fault types, resistances, inception angles, and locations.