Systems (100) and methods (600) for making a marker. The methods comprise: obtaining a resonator material which has been annealed under a tensile force selected to provide a maximum resonant amplitude at a bias field Hmax in the marker; and providing with the bias material of the marker an operating bias field Hoperating with a value less than a value of said bias field Hmax. The value of Hoperating is reduced by performing at least one of the following operations: selectively modifying a geometry of a bias material which is to be disposed in a housing of the marker; selectively modifying a spacing between the resonator material and the bias material arranged in a stacked configuration; and partially de-gaussing the bias material subsequent to being fully saturated.