For Title VII case, this does not violate due process. A jury found the employer liable for sexual harassment and awarded only nominal damages (one dollar) plus $868,750 in punitive damages. The trial court cut the punitive damages to $300,000 due to a statutory cap. On appeal to the 9th Circuit, a three judge panel found the amount of punitives was constitutionally excessive and reduced the award to $125,000.
The en banc 9th Circuit resinstated the $300,000 punitive damages award. State of Arizona v. ASARCO LLC (9th Cir en banc 12/10/2014).
The 9th Circuit explicitly declined to "rigidly apply" the three guideposts set out by the US Supreme Court in BMW v. Gore, 517 U.S. 559 (1996). Why? Because the 9th Circuit was dealing with a statute that "rigidly dictates the standard a jury must apply in awarding punitive damages and narrowly caps hard-to quantify compensatory damages and punitive damages." Thus, there is a satisfaction of the Supreme Court's concern that a defendant “receive fair notice not only of the conduct that will subject him to punishment, but also the severity of the penalty” that may be imposed.
AS the 9th Circuit summarized it:
The statute [42 U.S.C. § 1981a] provides specific notice of proscribed conduct. It specifies the maximum amount of damages that can be awarded, and incorporates both specified compensatory and punitive damages within the cap. The $300,000 dollar amount of the cap provides an extremely limited potential for recovery, and has not changed, nor been adjusted for inflation, since its adoption in 1991. There is nothing in our consideration of the Gore factors that would alter that conclusion.