La0.7Sr0.3MnO3 is predicted to show half-metallic behaviour at low temperature, which gives rise to a metallic character for one spin direction and an insulating character for the other. This 100% polarisation of the conduction band should enhance the spin dependent tunnelling in manganite-based tunnel junctions. La0.7Sr0.3MnO3/SrTiO3 epitaxial superlattices were grown on LaAlO3(001) substrates by metal-organic chemical vapour deposition (MOCVD). These multilayers consist of 15 epitaxial bilayers of La0.7Sr0.3MnO3 and SrTiO3. The junctions were patterned using UV lithography and Ar ion milling to carry out transport measurements in the current perpendicular-to-plane geometry (CPP). A temperature-independent non-linear I-V curve, which is characteristic of a tunnelling conduction mechanism, was observed below 50 K. At higher temperatures, the I-V curves are found to become linear and temperature-dependent. Up to 30 K, a constant tunnel magnetoresistance (TMR) (3%) is measured. The switching field is consistent with the film coercive field (a few 10s of mT). At higher temperatures, the TMR decreases rapidly. This temperature dependence is compared to the expected behaviour of a spin tunnel junction with half-metallic electrodes, with thermal activation or the loss of spin polarisation taken into account.