In preparation of the Large Hadron Collider (LHC) upgrade to High Luminosity LHC (HL-LHC), a number of new Nb3Sn magnets, including short model and prototype magnets, had to be electrically qualified. The process included a number of well-established Electrical Quality Assurance (ELQA) tests, such as electrical continuity checks of the magnet instrumentation, high-voltage (HV) insulation tests of the magnet and quench heater circuits, and impedance measurements. In certain cases, in order to fully understand the observed effects, we needed to introduce new measurement techniques, in particular both an impedance measurement at specific frequency and a HV insulation test of the quench heaters during high-current quenches of the magnet. Furthermore, in order to localize possible insulation faults, we performed HV insulation tests using an additional multichannel acquisition system with high sampling rate. In this contribution we present in detail the used measurement techniques, explain the safety aspects, and discuss the results and possible further work.