One illustrative method disclosed herein includes forming at least one layer of insulating material above a conductive structure, forming a patterned hard mask comprised of metal above the layer of insulating material, performing at least one etching process to define a cavity in the layer of insulating material, forming a layer of sacrificial material so as to overfill the cavity, performing at least one planarization process to remove a portion of the layer of sacrificial material and the patterned hard mask while leaving a remaining portion of the layer of sacrificial material within the cavity, and removing the remaining portion of the layer of sacrificial material positioned within the cavity.