No Stolen Trademarks Honored in America Act - Amends the Department of Commerce and Related Agencies Appropriations Act, 1999 to prohibit U.S. courts from recognizing, enforcing, or otherwise validating any assertion of rights by an individual (under current law, by a designated Cuban national) of a mark, trade name, or commercial name that was used in connection with a business or assets that were confiscated by the Cuban government unless the original owner of such mark or name, or such owner's bona fide successor, has expressly consented. Applies such prohibition only if the individual asserting the rights knew or had reason to know at the time of acquiring the rights asserted that the mark or name was the same or substantially similar to the mark or name used in connection with the business or assets that were confiscated.