I don't know anything about California state law, and I am not a lawyer. However, I have been asked this question in the past, regarding the value of NSXs, and I have discussed it with insurance folks and lawyers.
What you would need to do is to "prove" (I think this is normally done through the testimony of expert appraisers) that a car that has been damaged but completely and properly repaired has a market value that is lower than a car that has never been damaged. Unfortunately - like it or not - most experts will tell you that there is no reduction in market value when a car is in an accident and properly repaired.
Basically, the procedure you would use to gain any increase in the settlement from the insurance company would be to try negotiating directly with them on the settlement. Provide any evidence to justify the market value of the car, including whatever justification and expert testimony towards the difference between an accident-free car and a repaired car. If you are not able to come to an agreement with the insurance company, you would then need to take them to court to sue them, either yourself in pro se ("small claims") court, or using a lawyer.
The bottom line is that it's difficult if not impossible to recover damages due to diminished value - but the good news is that it's because your car probably doesn't lose all that much if any market value, even though it sucks when you've been trying to keep your car absolutely showroom-perfect.
