Capacitor and contact structures are provided, as well as methods for forming the capacitor and contact structures. The methods include, for instance, providing a layer of conductive material above a conductive structure and above a lower electrode of a capacitor; etching the layer of conductive material to define a conductive material hard mask and an upper electrode of the capacitor, the conductive material hard mask being disposed at least partially above the conductive structure; and forming a first conductive contact structure and a second conductive contact structure, the first conductive contact structure extending through an opening in the conductive material hard mask and conductively contacting the conductive structure, and the second conductive contact structure conductively contacting one of the lower electrode of the capacitor, or the upper electrode of the capacitor.