Only superconductors have zero resistance. Typically, that happens under rather special conditions, such as very low temperature and special materials.
But zero resistance (and it really is zero, as far as anyone has been able to determine) does not mean zero impedance. If you connect a voltage source across a superconductor a voltage will appear due to the inductance. The current will start off at zero and increase. When it reaches the critical current Jc the superconductor will go normal and will no longer have zero resistance. If you short the superconductor before that point, the current will circulate in the conductor forever, causing a magnetic field.
