It is not unusual for U.S. Courts to award large sums of punitive damages against state sponsors of terrorism.  Iran in particular has been hit with many such awards.  These awards are not contested by the foreign states and, to my knowledge, have never been enforced.  They seem purely symbolic. 

This Lawfare article argues that such awards are bad public policy and “pose[] a threat to the peaceful international legal order” by placing the United States in a position of primacy over all other nations.  The author argues that Congress should amend the Foreign Sovereign Immunities Act to disallow punitive damages against foreign states.