We present electromagnetic models aiming to calculate the variation of the inductance in a magnet due to dynamic effects such as the variation of magnetization or the coupling with eddy currents. The models are studied with special regard to the calculation of the inductance in superconducting magnets which are affected by interfilament coupling currents. The developed models have been compared with experimental data coming from tests of prototype magnets designed for the new generation of accelerators. This work is relevant for the quench protection study of superconducting magnets: quench is an unwanted event, when part of the magnet becomes resistive; in these cases, the current should be discharged as fast as possible, in order to maintain the resistive zone temperature under a safe limit. The magnet inductance is therefore a relevant term for the description of the current discharge, especially for the high-field new generation superconducting magnets for accelerators, and this work shows how to calculate the correct value during rapid current changes, providing a mean for simulations of the reached temperature.