Shielding is highly conductive, dissipating the external field as eddy currents.
That's a copper box to you, chief.
Technology is straightforward compared to this
CMS detector at CERN. 50 foot high, 100 000x Earth's field, weighs 12 500 tons, cooled to -271 degrees. Quite green too, using titanium recycled from Soviet subs and bits of old NATO artillery shells.
Data from this has probably accelerated railgun development.