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 and thus left the 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.
“We now have a dog and Alistair is still the dumbest one in the party.” — Morrigan This article contains spoilers for Dragon Age: Origins. Click here to reveal them.
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.