A class of molecular ribbons, with almost-ideal charge transmission, that is weakly dependent on the anchoring structure or electrode crystalline orientation and easy to synthesize has been identified. Charge transport through two sets of aromatic nanoribbons, based on the pyrene and perylene motifs, has been investigated using density functional theory combined with the nonequilibrium Green's function method. The effects of wire length and multiple terminal thiolate groups at the junction with gold leads have been examined. For the oligopyrene series, an exponential drop in the conductance with the increase of the wire length is found. In contrast, the oligoperylene series of nanoribbons, with dual thiolate groups, exhibits no visible length dependence, indicating that the contacts are the principal source of the resistance. Between the Au(001) leads, the transmission spectra of the oligoperylenes display a continuum of highly conducting channels and the resulting conductance is nearly independent of the bias. The predictions are robust against artefacts from the exchange-correlation potential, as evidenced from the self-interaction corrected calculations. Therefore, oligoperylene nanoribbons show the potential to be the almost-ideal wires for molecular circuitry. © 2011 American Physical Society.