Zhege
361
Insured shipping
In the US, there are several third party insurers. I have been using Parcel Pro - they focus on watches and jewelry. They primarily work with professional sellers, but are happy to sign up enthusiasts / amateur sellers that have infrequent high value shipments. They are very easy to work with and an actual person (!) will work with you over the phone and on your early shipments to make sure you are doing things correctly. They provide a lot of guidance to help protect you against fraud as well.
Once you are set up, you can do everything on-line. You print out a FedEx label, bring your package to a staffed location (so you get a receipt for the package) and can track the package on the FedEx website. The rates seem very reasonable. As you may know, FedEx will not insure watches / jewelry above $500. With ParcelPro (or other third party insurer) you have all the ease of using FedEx (or UPS) with the ability to insure high value shipments.
I have no experience with the responsiveness on claims, but given that a lot of sellers here and on other websites use them, I felt comfortable shipping a Rolex Daydate a few months back. Not quite a PC-chrono, but still something I wouldn't want to risk losing in shipping. I have a Patek annual that needs a service, but I'm going to bring that the HSWA in person next time I go to NYC so I can see their new operation and find the perfect replacement strap for that watch 
patek service process
Servicing perpetual chronos
My experience