We investigate the potential of submm-mm and submm-mm-radio photometric redshifts using a sample of mm-selected sources as seen at 250, 350 and 500μm by the SPIRE instrument on Herschel. From a sample of 63 previously identified mm sources with reliable radio identifications in the Great Observatories Origins Deep Survey North and Lockman Hole North fields, 46 (73 per cent) are found to have detections in at least one SPIRE band. We explore the observed submm/mm colour evolution with redshift, finding that the colours of mm sources are adequately described by a modified blackbody with constant optical depth τ= (ν/nu0)β, where β=+1.8 and ν0=c/100 μm. We find a tight correlation between dust temperature and IR luminosity. Using a single model of the dust temperature and IR luminosity relation, we derive photometric redshift estimates for the 46 SPIRE-detected mm sources. Testing against the 22 sources with known spectroscopic or good quality optical/near-IR photometric redshifts, we find submm/mm photometric redshifts offer a redshift accuracy of |Δz|/(1 +z) = 0.16 (<|Δz|>= 0.51). Including constraints from the radio-far-IR correlation, the accuracy is improved to |Δz|/(1 +z) = 0.15 (<|Δz|>= 0.45). We estimate the redshift distribution of mm-selected sources finding a significant excess at z > 3 when compared to ˜ 850 μm selected samples.