Contact resistance between electrically connected parts of electronic elements can negatively affect their resulting properties and parameters. The contact resistance is influenced by the physicochemical properties of the connected elements and, in most cases, the lowest possible value is required. The issue of contact resistance is also addressed in connection with the increasingly frequently used carbon allotropes. This work aimed to determine the factors that influence contact resistance between graphene prepared by chemical vapour deposition and pre-patterned Cu and Au electrodes onto which graphene is subsequently transferred. It was found that electrode surface treatment methods affect the resistance between Cu and graphene, where contact resistance varied greatly, with an average of 1.25 ± 1.54 kΩ, whereas for the Au electrodes, the deposition techniques did not influence the resulting contact resistance, which decreased by almost two orders of magnitude compared with the Cu electrodes, to 0.03 ± 0.01 kΩ.