The best replacement for punitive damages is compensatory damages.

The best alternatives to punitive damages are rated as following:
★★★★★  compensatory damages
★★★  actual damages
★★  nominal damages
★★  compensatory
★  restitution
★  exemplary damages
★  liquidated damages
★  pain and suffering

Your alternative for punitive damages is not listed? Suggest!
Speaking about punitive damages, one probably shouldn't forget about suing.

Other search terms related to punitive damages and their ratings are:
★★★★★ suing
You have in mind a companion for punitive damages and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of punitive damages in all years. Click on graph for more.
punitive damages
compensatory damages
actual damages