One method disclosed herein includes forming first and second transistor devices in and above adjacent active regions that are separated by an isolation region, wherein the transistors comprise a source/drain region and a shared gate structure, forming a continuous conductive line that spans across the isolation region and contacts the source/drain regions of the transistors and etching the continuous conductive line to form separated first and second unitary conductive source/drain contact structures that contact the source/drain regions of the first and second transistors, respectively. A device disclosed herein includes a gate structure, source/drain regions, first and second unitary conductive source/drain contact structures, each of which contacts one of the source/drain regions, and first and second conductive vias that contact the first and second unitary conductive source/drain contact structures, respectively.