I`m trying to think of a good example, one of wich are fuel injectors.
If you run a low impeadance injector with constant high crurrent instead of the high current opening, lower holding current, it will take longer to close.
As the magnetic field colapses it has more "momentum" stored which need to overcome.

The volatage is rate of change of magnetic flux. When saturated this rate of change is not as fast so the voltage is less.

Darren