The optimization of contacts between graphene and metals is important for many optoelectronic applications. In this work, we evaluate the contact resistance and sheet resistance of monolayer and few-layered graphene with different metallizations using the transfer length method (TLM). Graphene was obtained by the chemical vapor deposition technique (CVD-graphene) and transferred onto GaAs and Si/SiO2 substrates. To account for the quality of large-area contacts used in a number of practical applications, a millimeter-wide TLM pattern was used for transport measurements. Different metals—namely, Ag, Pt, Cr, Au, Ni, and Ti—have been tested. The minimal contact resistance Rc obtained in this work is 11.3 kΩ μm for monolayer CVD-graphene, and 6.3 kΩ μm for a few-layered graphene. Annealing allows us to decrease the contact resistance Rc and achieve 1.7 kΩm μm for few-layered graphene on GaAs substrate with Au contacts. The minimal sheet resistance Rsh of few-layered graphene transferred to GaAs and Si/SiO2 substrates are 0.28 kΩ/□ and 0.27 kΩ/□. The Rsh value of monolayer graphene on the GaAs substrate is 8 times higher (2.3 kΩ/□), but it reduces for the monolayer graphene on Si/SiO2 (1.4 kΩ/□). For distances between the contacts below 5 μm, a considerable reduction in the resistance per unit length was observed, which is explained by the changes in doping level caused by graphene suspension at small distances between contact pads.