Here's information regarding baggage carriage for Northwest:
Limits of Liability For customers who have traveled on a domestic itinerary (defined as the 48 contiguous United States, Alaska and Hawaii) liability for the loss of, damage to, or delay in the delivery of personal property or luggage is
limited to $2,500 per ticketed passenger, unless a higher value was placed on the luggage and applicable charges were paid at the time the property was checked into Northwest's care.
You can read their entire "contract of carriage" here if you wish to:
http://www.nwa.com/plan/contract2.pdf
"When I reached my destination, all the case latches and edging were ripped off, hinges bent, and the tuba inside sustained $4300 of damage."
It makes a difference where you got your $4300 figure, additionally EVERYTHING needs to be in writing...repair estimates, new case cost, potential new tuba cost, etc., etc., etc.
Insurance
An absolute must. Flying or not. Get your horn, gigbag, case, etc. insured. Do it either for what you paid (must provide invoice) or replacement cost, which is what I would suggest. Be sure that it covers theft, vandalism, fire, airline damage, etc., etc., etc. My policy covers everything except insect infestation (honestly...) and it's only $200 something-or-other a year for two horns, flight cases, and gig bags.
Case
If your're going to fly, you have to have one of these:
This won't cut it:
Documentation:
Take tons of pictures before you ever leave on a flight with a camera that can date stamp. Then take pictures of how the horn was packed. It's not a gaurantee that they'll cave in, but pictures never seem to hurt.
Tickets vs. Flight Cases
Yes, some people have purchased seats for their horns and have flown right next to them all over the world. However, for most people that just isn't practical. Buying 1 or 2 seats for a horn, getting them through the airports, security is a bear (good luck getting them through the x-ray machine templates), and actually getting the counter agent and flight attendants to let you take it on the plane is a hastle and a half. On the other hand, getting a flight case on the plane only requires dealing with one person, one time and often additional costs can be totally avoided and it can be loaded as a regular piece of checked baggage. Get a good, real flight case that fits well, pack it carefully, lock it after the inspections. No, it doesn't prevent the horn from being stolen or from being run over by a freak bulldozer that happens to be on the runway, but I think the practicality factor is huge here and that buying seats for tubas is an even bigger risk (what would you do if they refused to allow you to 'seat' your tuba?) than checking them in a flight case.