The electrical conductance through a ring is sensitive to the threading magnetic flux. It contains a component that is periodic with an Aharonov-Bohm (AB) period equal to the quantum flux. In molecular/atomic loops on the nanometer scale, encircling very small areas, the AB period involves unrealistically huge magnetic fields. We show that despite this, moderate magnetic fields can have a strong impact on the conductance. By controlling the lifetime of the conduction electron through a preselected single state that is well separated from other states due to the quantum confinement effect, we demonstrate that magnetic fields comparable to 1 Tesla can be used to switch a nanometric AB device. Using atomistic electronic structure calculations, we show that such effects can be expected for loops composed of monovalent metal atoms (quantum corrals). Our findings suggest that future fabrication of nanometric magnetoresistance devices based on the AB effect is feasible.