The *best* time to get insurance coverage for shipping is when you first buy the instrument. At that point, with a fresh new receipt in hand, you'll get no hassles with regard to the valuation of the instrument. Although insurance fraud at this point isn't unheard of, if it's a regular sort of transaction I don't think the insurer will question what you paid as the market price replacement value.
Then minute you own the instrument and are shipping it to yourself, you're in for a much harder time it's much harder to authenticate your claimed value, especially on high dollar instruments like these. You may have paid $8000 for an instrument when it was new 10 years ago, but you may be in for a debate as to whether it's worth $4000 now or $10000.
The problem is that it's not the insurer's job to establish or verify the value of an instrument - the shipping agent will gladly take your word for it and sell you the insurance, but that doesn't guarantee that the adjuster will pay you the amount of insurance you purchased if there's a claim.
Furthermore, there's a much better chance of your instrument getting damaged than destroyed, and you may have to go around in circle to have a discussion about the cost of repairs and the effect on the value of the instrument if it is repaired.
If you buy a Mexican J-bass for $300 and love it more than your pre-CBS Jazz that's appraised at $10,000 that's great for you, but if you try to insure the Mexi-J for $5000, you're probably in for an unpleasant shock if you have to make a claim.
David Fung