If you’ve got to take something valuable, especially something fragile and valuable, on a plane, it’s best to try to carry it on. If you must check in then be sure to look at your bags before you leave the baggage claim area, just in case that item has gotten damaged or disappeared.
Most airlines recommend to do so on their websites. For example, this is what Delta’s website say – “If you feel your baggage was damaged during a flight bring it to the Delta Air Lines airport baggage office immediately after the arrival of your flight. All damages should be reviewed and evaluated by the baggage service office personnel.”
Calling a CSR or tweeting about it will get you the same answer; or something on the lines of “Normally we would say no, unless you do have delicate items in the bag. Just in case.” Readers have complained that failing to report at the airport can lead to CSRs pointing you to their websites and company polices.