Necessarily with a large EMP, as the energy is stored in the magnetic field.

Fortunately the energy density[0] is comparable with rubber bands[1] and supercapacitors[1], so while the EMP is large, it's not terrifyingly large.

[0] at least according to wikipedia, 4-40 kJ/kg: https://en.wikipedia.org/wiki/Superconducting_magnetic_energ...

[1] 1.6-6.6 kJ/kg and 10-30 kJ/kg respectively: https://en.wikipedia.org/wiki/Energy_density

The energy density isn't the scary bit, the power density is. The referenced paper in that Wikipedia article indicates ~10^5 higher power density than li-ion. So while it stores 10x less energy than li-ion it dumps it so much faster. The difference between a combustion and a detonation if you will. I'm guessing the vicinity of the thing would get turned to plasma.

A very small and localised plasma near the normal conductors that suddenly experience a rapidly decaying magnetic field; but the total energy is still (relatively) low compared to, say, the thermal heat capacity of the air of about 1.3 kJ/K/m^3.

That energy density number likely includes the cooling system.

That is what I thought too, but reading the paper referenced it seemed like they only included the coils, not even the support structure to keep them from collapsing. But it wasn't that clear.

Edit: they were clear that the limiting factor on energy and power density was the forces exerted on the coils.