No Stolen Trademarks Honored in America Act This bill modifies the bar against U.S. courts enforcing or validating trademarks that were confiscated by the Cuban government. The bill prohibits U.S. courts from enforcing or validating such confiscated trademarks if the mark had been used in connection with a confiscated business or asset. Currently, the prohibition applies only if the confiscated trademark is being asserted in the United States by a Cuban national. Under the bill, the prohibition shall not apply if the original trademark owner, or a successor, has expressly consented to the enforcement action. The prohibition shall apply only if the entity asserting the trademark rights knew or should have known, when it acquired the rights, that the mark was the same or substantially similar to one connected to a confiscated business or asset.