Short chains of porphyrin molecules can mediate electron transport over distances as long as 5-10 nm with low attenuation. This means that porphyrin-based molecular wires could be useful in nanoelectronic and photovoltaic devices, but the mechanisms responsible for charge transport in single oligo-porphyrin wires have not yet been established. Here, based on electrical measurements of single-molecule junctions, we show that the conductance of the oligo-porphyrin wires has a strong dependence on temperature, and a weak dependence on the length of the wire. Although it is widely accepted that such behaviour is a signature of a thermally assisted incoherent (hopping) mechanism, density functional theory calculations and an accompanying analytical model strongly suggest that the observed temperature and length dependence is consistent with phase-coherent tunnelling through the whole molecular junction.