Yes, the United States Supreme Court has held that the Due Process Clause of the Fourteenth Amendment no state shall deprive a person of life, liberty or property without due process of law imposes limitations on punitive damage awards. The Due Process Clause prohibits awards that are grossly excessive, because such awards fail to provide fair notice to a defendant of the penalty he or she might have to face. The Due Process Clause also prohibits states from punishing defendants for injuries caused to persons not before the court (persons who are not litigants or parties to the litigation).
For example, in BMW v. Gore (1994) the U.S. Supreme Court ruled that a $2 million dollar punitive damage award against a car manufacturer for failing to disclose that a BMW had been repainted was grossly excessive when the actual damages to the plaintiff were only $4,000. Elementary notions of fairness enshrined in our constitutional jurisprudence dictate that a person receive fair notice not only of the conduct that will subject him to punishment, but also of the severity of the penalty that a State may impose, the Court wrote.
In Philip Morris USA v. Williams (2007), the U.S. Supreme Court reversed a jury’s $79.5 million punitive damage verdict against a cigarette manufacturer for negligence and deceit (two torts). The Court reasoned that the Due Process Clause prohibits the award of punitive damages against a defendant based upon injuries to persons who are strangers to the litigation.