Both plants have their own type of personal space issues, not liking to share due to their allelopathic tendancies and preference for a drier spot in the garden. Together however they muddle along very nicely, a clash of colours, which provide wonderful backdrops of colour most of the year round.
"Dropmore" Catmint offers silvery foliage, scented and not so popular with the wallabies. Lilac blue flowers in Spring and Autumn are on upright stems, and if grown in full sun will remain upright (unlike the larger Catmint cultivars).
"Oriental LImelight" Artemisia (or wormwood), also likes a full sun location in drier poorer soils. Flowers are insignificant compared to the bright foliage. Dried leaves can be used in the cupboard to deter moths, while fresh foliage can be used to help worm chickens (or if planted near cage they will self medicate).
Water both plants as needed in the hotter months, prune back hard to the crown immediately when they drop their foliage and they will flourish back.