One illustrative method disclosed herein includes, among other things, forming a first conductive structure and a second conductive structure that is conductively coupled to the first conductive structure. In this example, forming the second conductive structure includes forming a ruthenium cap layer on and in contact with an upper surface of the first conductive structure, with the ruthenium cap layer in position, forming a liner layer comprising manganese on and in contact with at least the surfaces of the second layer of insulating material, wherein an upper surface of the ruthenium cap layer is substantially free of the liner layer, and forming a bulk ruthenium material on and in contact with the liner layer, wherein a bottom surface of the bulk ruthenium material contacts the upper surface of the ruthenium cap layer.