  Superconducting shields are commonly used to suppress external magnetic
interference. We show, that an error of almost an order of magnitude can occur
in the coil-factor in realistic configurations of the solenoid and the shield.
The reason is that the coil-factor is determined by not only the geometry of
the solenoid, but also the nearby magnetic environment. This has important
consequences for many cryogenic experiments involving magnetic fields such as
the determination of the parameters of Josephson junctions, as well as other
superconducting devices. It is proposed to solve the problem by inserting a
thin sheet of high-permeability material, and the result numerically tested.
