The cryoEDM neutron electric dipole moment experiment requires a SQUID magnetometry system with pick-up loops inside a magnetically shielded volume connected to SQUID sensors by long (up to 2m) twisted-wire pairs (TWPs). These wires run outside the main shield, and therefore must run through superconducting capillaries to screen unwanted magnetic pick-up. Superconducting capillaries can be produced by extruding the flux core of solder wire. After heating the solder wire in turpentine for an extended period of time, the flux is removed and a wire can be threaded through lengths of up to 1m. We show that the average measured transverse magnetic pick-up of a set of lengths of TWPs is equivalent to a loop area of 5.0×10 −6 m 2 /m, or 14 twists per metre. From this we set the requirement that the magnetic shielding factor of the superconducting capillaries used in the cryoEDM system must be greater than 2.0×10 4 . The shielding factorthe ratio of the signal picked-up by an unshielded TWP to that induced in a shielded TWP was measured for a selection of capillaries. We conclude the transverse shielding factor of a uniform capillary is greater than 10 7 . The measured pick-up was equal to, or less than that due to direct coupling to the SQUID sensor (measured without any TWP attached). We show that discontinuities in the capillaries substantially impair the magnetic shielding, yet if suitably repaired, this can be restored to the shielding factor of an unbroken capillary. We have constructed shielding assemblies for cryoEDM made from lengths of single core and triple core solder capillaries, joined by a shielded Pb cylinder, incorporating a heater to heat the wires above the superconducting transition as required.