We have developed two novel vapour phase transport methods to grow ZnO nanorod arrays isotopically enriched with O-18. Firstly, a three-step process used to grow natural and Zn-enriched ZnO nanorods has been further modified, by replacing the atmospheric O-2 with enriched O-18(2), in order to grow O-18-enriched ZnO nanorods using this vapour-solid method on chemical bath deposited buffer layers. In addition, O-18-enriched ZnO nanorods were successfully grown using O-18 isotopically enriched ZnO source powders in a vapour-liquid solid growth method. Scanning electron microscopy studies confirmed the success of both growth methods in terms of nanorod morphology, although in the case of the vapour-liquid-solid samples, the nanorods' c-axes were not vertically aligned due to the use of a non-epitaxial substrate. Raman and PL studies indicated clearly that O-enrichment was successful in both cases, although the results indicate that the enrichment is at a lower level in our samples compared to previous reports with the same nominal enrichment levels. The results of our studies also allow us to comment on both levels of enrichment achieved and on novel effects of the high temperature growth environment on the nanorod growth, as well as suggesting possible mechanisms for such effects. Very narrow photoluminescence line widths, far narrower than those reported previously in the literature for isotopically enriched bulk ZnO, are seen in both the vapour-solid and vapour-liquid-solid nanorod samples demonstrating their excellent optical quality and their potential for use in detailed optical studies of defects and impurities using low temperature photoluminescence.