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Conductance of zigzag interfaces between a graphene sheet and a normal metal is investigated in the tight-binding approximation. Boundary conditions, valid for a variety of scattering problems, are constructed and applied to the normal-metal–graphene–normal-metal junctions. At the Dirac point, the conductance is determined solely by the evanescent modes and is inversely proportional to the length of the junction. It is also independent of the interface resistance. Away from the Dirac point, the propagating modes’ contribution dominates. We also observe that even in the junctions with high interface resistance, for certain modes, ideal transmission is possible via Fabry-Pérot-like resonances.