Reliable measurement of electrical charge transport in molecular layers is a delicate task that requires establishing contacts with electrodes without perturbing the molecular structure of the film. We show how this can be achieved by means of novel device consisting of ultra-flat electrodes separated by insulating material to support the molecular film. We show the fabrication process of these electrodes using a replica technique where gold electrodes are embedded in a silicon oxide film deposited on the angstrom-level flat surface of a silicon wafer. Importantly, the co-planarity of the electrode and oxide areas of the substrate was in the sub-nanometer range. We illustrate the capabilities of the system by mapping the distribution of electrical transport pathways in molecular thin films of self-assembled oligothiophene derivatives using conductive atomic force microscopy. In comparison with traditional bottom contact non-coplanar electrodes, the films deposited on our electrodes exhibited contact resistances lower by a factor of 40 than that of the similar but non-coplanar electrodes.