Insurance is definitely one of those damned if you do, really damned if you don't things.
If you make money playing your instrument, then you need to have coverage for professional use (often available through musician's union, but there are lots of private instrument insurance specialists as well). The coverage value is determined by professional appraisal which you would want to repeat every year or two.
If you don't make money playing your instrument, then it can be covered under your homeowner's or renter's insurance, but the insurance company may impose coverage limits for instruments of high or collectable value. So, your Mexican Fender Jazz would be fully covered, your US Fender Jazz would probably be fully covered, and your new Alembic Series bass probably would not.
In this case, you establish the value of the instrument by professional appraisal then have a discussion with the insurance agent about how much special coverage you require. This is exactly like coverage for jewelry - there's some nominal limit of coverage (often around $5000) and anything more requires proof and additional premium.
Your receipt is a pretty good valuation initially and would not be contested if it's less then the limit of your policy. After time, they may try to argue that the value of your instrument is lower because of wear, but if the instrument is still in production, there will also be many market indicators of what a similar new or used instrument sells for.
If you want to argue that rarity or collectibility have increased the value of your instrument over the time you've held it, you'll need a professional appraisal to back that up as well as having purchased additional coverage for the incremental amount. This is not an unusual occurance (collectibles are always climbing and dropping).
One thing that doesn't help you much is if the new price of an instrument has radically increased over the years. If you bought a new Alembic last year for $10,000 and it's stolen, then it's likely that you might see $11,000 to replace it if you had appropriate coverage. But if you bought your Alembic new 10 years ago for $6000, you aren't going to get $11,000 now. If you bought a used 10 year old instrument for $2000 last year, then you should be able to get $2000 back, but the lofty prices of new instruments aren't a factor in a settlement. The only effect you'll see there is that the high new instrument prices might raise the current used prices a bit, but that's only a tiny fraction of the new price change. Although you see people asking $8000 for a used instrument that would cost $12,000 it's pretty rare that a sale like that ever closes without other factors (famous owner, etc.). Because of the way that the resale market works, you might pay $12,000 for a new instrument but recover only $3000-4000 if you immediately put it up for sale. The reality of pricing is what the pro appraisal is trying to reflect, with an eye toward condition of your instrument and some sense of the pulse of the used market.
The final gotcha here is that the insurance agent is not particularly helpful at any point in the transaction. He's not going to volunteer that there are limits on your generic coverage unless you specifically ask, since that improves their ability to limit your claim in the future. If you're pursuing specialized coverage, he's not going to help you determine the proper valuation (beyond directing you to find an appraiser), again to limit liability. And if you decide that you want to purchase some huge amount of coverage just to be sure, he'll happily sell it to you, but not tell you that you have to have an appraisal to establish the value in the event of a loss. There's nothing that stops you from insuring your beloved bass for $20,000, but if your only proof of value is a receipt that you paid $2000 for it, you're just throwing your money away.
David Fung