High-temperature superconductor (HTS) is an enabling technology for ultra-high-field magnets and compact fusion reactors. In recent years, rare earth-barium-copper-oxide (REBCO) coated conductor outstands the HTS candidates in terms of superior current-carrying capacity and the potential for massive production at low costs. However, REBCO conductor technology has obstacles to overcome before massive application: REBCO wires often exhibit critical current (Ic) fluctuations along the tape length. Defects in the REBCO wires introduced during manufacturing can go unnoticed and contribute as weak points prone to quench initiation. Therefore, a system capable of inspecting/characterizing the conductor performance over length is essential for (1) the full-cycle quality control and assurance of REBCO HTS magnets; and (2) providing feedback information for improving REBCO conductor manufacturing. Here we present the development of reel-to-reel REBCO characterization systems based on the magnetization behavior of the superconductor, assessing the Ic of HTS tapes in a contact-free, non-destructive approach. The inspection systems first magnetize the tape-form HTS wire at cryogenic temperature using a magnetic field perpendicular to its wide surface, inducing a persistent screening current loop in the tape. A magnetic field probe then records the induced screening-current field signal. We present two field probe designs: (1) scanning Hall probe for mapping the screening-current field with a high spatial resolution, targeting 100-m-class laboratory-scale REBCO conductors; and (2) magnetic circuit for detecting screening-current magnetic moment with high scanning speed, targeting kilometer-class industrial-scale conductors. We demonstrate and compare systems adopting these two designs, which have entered service in both academia and industry.