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We investigate the contact resistivity of p-type passivating contacts for silicon solar cells. Our contact structures are compatible with firing, a rapid annealing process similar to the one used for sintering of the screen-printed metallisation in solar cell manufacturing. We find that the short firing process crystallises the doped layers and incorporates active boron dopants up to the solubility concentration at the chosen firing temperature. The dependence of our contact resistivities on carrier density and temperature suggest that the hole transport is a combination of tunnelling through the oxide at the wafer surface and of thermionic field emission over the Schottky barrier to the metallisation. For ideal firing conditions we find implied open circuit voltages up to 720 mV and contact resistivities as low as 15 mΩcm2.