© Published under licence by IOP Publishing Ltd. The magnetizations of eight high-gradient quadrupole cables designated HQ and QXF and a pair of strands, identical in architecture but with different effective strand diameters extracted from an HQ and a related QXF cable, were measured. In the service of field quality assessment, the cable magnetizations and losses were measured by pickup coil magnetometry at 4.2 K in face-on fields, B m , of ± 400 mT at frequencies, f, of up to 60 mHz. Based on the coupling component of loss, Q coup , the coupling magnetization M coup = Q coup /4B m was derived for a ramp rate of 7.5 mT/s. Persistent current (shielding) magnetization and loss (M sh and Q h,strand ) were measured on short pieces of extracted strand by vibrating sample magnetometry at 4.2 K. Unpenetrated M-B loops to ±400 mT and fully penetrated loops to ±14 T were obtained. M coup can be easily controlled and reduced to relatively small values by introducing cores and adjusting the preparation conditions. But in low fields near injection Nb3Sn's high J c and correspondingly high M sh,cable may call for magnetic compensation to preserve field quality. The suitably adjusted cable and strand fully penetrated M-B loops were in reasonable accord leading to the conclusion that strand magnetization is a useful measure of cable magnetization, and that when suitably manipulated can provide input to magnet field error calculations.