One device disclosed herein includes a gate above a semiconductor substrate, the gate comprising a gate structure and a gate cap, and conductive source/drain metallization structures adjacent the gate, each of the conductive source/drain metallization structures having a front face and a recess defined in each of the conductive source/drain metallization structures. In this example, the device further includes a spacer structure comprising recess filling portions that substantially fill the recesses and a portion that extends across a portion of the upper surface of the gate cap, wherein a portion of the gate cap is exposed within the spacer structure, an insulating material within the spacer structure and on the exposed portion of the gate cap, a gate contact opening that exposes a portion of an upper surface of the gate structure, and a conductive gate contact structure in the conductive gate contact opening.