The relaxation of the shielding current-induced magnetic moment in YBa(2)Cu(3)O(7) thin films, which were grown in situ, is studied as a function of temperature. Although typical relaxations cause a large amount of decay in the magnetic shielding current (on the order of 10 to 20 percent for the first 1000 seconds), it is shown that this is not necessarily a serious problem for applications such as magnets operating in persistent-current modes. This is because the decay of the magnetic shielding current depends sensitively on how far away the operating current density is from the critical current density J(c). By using a quenching process the shielding current is reduced slightly below J(c) and the relaxation is dramatically reduced. A general relation between the relaxation rate at J(c) and the reduction of the relaxation rate upon lowering of the operating current is obtained and is shown to be consistent with experimental data.