A prominent member of House Ortan was Caridin, who created many things during his time and eventually rose up to Paragon status for creating the Anvil of the Void; he thus left House Ortan to found his own house. The house was formally declared extinct four hundred years ago during the Fourth Blight, when the Ortan Thaig fell to the darkspawn.
This section contains spoilers for: Dragon Age: Origins.
However, Orta is a surviving member of House Ortan, although she requires evidence to prove she is a true descendant.
If Paragon Caridin creates the crown for Orzammar's next king as part of A Paragon of Her Kind quest, he uses the ancient seal of House Ortan on the crown instead of the seal of his own house. See here.