Key to empathizing is asking if the customer is okay first and foremost. Make their experience seamless and encouraging. Let them know that the car will be back to its original beauty if not better. That they can trust you to treat the car with respect and that you will keep them in the loop throughout the process.
Your customer is in a fragile frame of mind and I think that once the effects of the shock pass, they will have a greater appreciation for you and the services you provide. In most cases, a person’s vehicle is the largest investment they have ever made. Not to mention that their vehicle may be the only means of putting food on the table of their loved ones. This unfortunate incident is huge to them, they need to know that they have just one person on their side and understanding their pain.
If you have ever had an accident like this then you know how frustrating it is. Now they have to go through the insurance company which we all know is an ordeal in itself and figure out if a rental car is covered so that there is no further interruption in their lives. Any way that you can smooth the road for them, you should. Contact the insurance company for them, get the paperwork rolling, get the approval and set out to be the solution to their problem.
This is where word of mouth starts, this is how to get your business up and rolling. Seize every opportunity to provide stellar customer service, not just for the money but also because it makes you a better person.