To study the effect of the substrate support on the nanoscale contact, three different regimes, i.e., graphene on rigid (ultra-crystalline diamond) and on elastic (Polydimethylsiloxane) supports and free-standing graphene, were considered. The contribution of the graphene support to the mechanical and electrical characteristics of the graphene/metal contact was studied using the conductive atomic force microscopy (AFM) technique.The results revealed that the electrical conductivity of the graphene/metal contact highly depends on the nature of the graphene support. The conductivity increased when transitioning from suspended to elastic and then to rigid substrates, which is attributed to the changes in the contact area being higher for the suspended graphene and lower for the rigid substrate. The experimental observations showed good agreement with theoretical results obtained from modeling of the studied material systems. Further, the results indicated that in addition to the substrate support, the nature of the contact, static or dynamic, results in large variations of the electrical conductivity of the graphene/metal contacts. In case of the static mode, the contact made with supported graphene was very stable for a wide range of applied normal loads. Transitioning to the dynamic mode led to instability of the graphene/metal contact as demonstrated by lowering in the electrical conductivity values. This transition was even more pronounced for free-standing graphene which is attributed to graphene sagging during rapid scanning of the tip over the graphene surface. This study creates a new knowledge on understanding of the nanoscale contacts forming with 2D materials thus enabling further advances in the applications of 2D materials in highly stable and reliable electronic devices.