In species complex, including these species on Artemisia:
Puccinia absinthii
Puccinia artemisiella

Puccinia tanaceti is a rust fungus that affects the leaves of Tansy, Feverfew and Mugwort (Tanacetum, Artemisia), with brown uredinia and darker telia on both sides of the leaf.  There is no host alternation, and spermogonia and aecia are not formed.  It is not considered to be a gall-causer.

Taxonomy is complex, and some authors consider that a range of different species affect Artemisia (P artemisiella, P absinthii) with P tanaceti only affecting Tanacetum speces - Tansy, Feverfew, etc.  Therefore this species is best treated as 'sensu lato' - in a broad sense. 

host

Photograph the rust on the host.  Ensure you have noted the host-plant species in your comments.  Microscopic examination is recommended

On Tanacetum and Artemisia

See 'Plant Parasites of Europe' website for more information on taxonomy and rusts on Artemisia