In general, servicing costs of an automatic/mechanical Cartier watch (this would include disassembly, oiling, cleaning parts, and then readjusting the watch for better time keeping) as well as replacing the crystal and crown would be pretty expensive. But as others have said, I would shop around. I would also contact an authorized Cartier servicing/watch repair. They should be able to give you an estimate, but it will likely be pretty high. Or, it's possible to find a jeweler who can just replace the crystal and crown and not do the rest of the servicing.
Scroll down to the bottom of this page below; they don't have the price of servicing a Cartier, but it will give you an idea of how expensive "servicing"-- cleaning, disassembling, polishing, adjusting, oiling, etc. can be: (and this isn't repairs, just regular maintenance).
Is watch servicing really that important? What’s inside a service operation? How much does it cost? Let's find out now dear watchgeeks!
blog.toolwatch.io
[edit: the cynic in me says certainly the jewelers are trying to get a bit more money by including servicing costs along with the repairs, but on the other hand, to do those repairs would require a lot of disassembly and it wouldn't make much sense to go through that process without giving the watch some basic servicing, akin to replacing the windshield and gear shift on your old car, but not doing an oil change, spark plug change, air filter change, etc. So, in my opinion if the watch is of value to your son, either for sentimental reasons (a future heirloom) or otherwise, I would just go ahead with the servicing]
www.seikowatches.com
www.seiyajapan.com
