We have developed and tested a novel magnetic inductive antenna for detecting and localizing quenches and flux jumps in superconducting accelerator magnets during ramping and steady-state operations. The antenna principle is based upon sensing temporal variation of the axial field gradient in the magnet bore that is specific to propagating quench. Two antenna configurations were developed and built, optimized respectively for sensing disturbances of the off-axis (for the dipole magnet) and axial (for the quadrupole magnet) gradient of the axial field. The antennas were qualified during tests of LBNL's high-field dipole, HD3b, and LARP's Nb3Sn quadrupole HQ02b. A reliable and accurate localization of quenches and flux jumps was demonstrated. Upon ramping up the magnet current, we observed peculiar dynamics of the magnetic disturbances travelling along the cable at velocities of ∼800 m/s. Also, details of slow quench propagation in the HQ02 quadrupole at a small fraction of operational current were detected and recorded.