Websites with advice (and check your airline’s website as well):

• Classic FM
• American Federation of Musicians
• TSA (from 2014)

Further tips from John Dornenburg: 

• When flying I either purchase a seat for my bass viol or check the instrument in my Stevenson flight-travel case. I do not think it is realistic these days to expect to take a bass viol into a plane’s cabin without a seat purchase. 
• TSA will need to open the case for inspection, so locking is not an option. 
• If the instrument is my only piece of checked baggage the airlines will often (but not always) waive the oversized baggage fee. Most recently I flew trans-Atlantic on British Airways and there was no extra fee for my checked instrument. On Norwegian Air I purchased a seat for the bass.
• I have not flown with treble or tenor instruments recently, but one should be able to take a treble into the cabin without serious challenge. A tenor is borderline. 
• Typical case measurements:
  • Treble case: 7” x 10” x 30”
  • Tenor case: 9” x 14” x 41”
  • Bass case: 12” x 18” x 53”
  • These are all well within the 150 inch limit, which is a standard for many airlines for checked luggage (length + height + width ≤ 150”. The weight is not an issue.
• Instruments are normally damaged by secondary impacts within the hard case. It is worth stressing that the viol should not be able to move in any direction within the case. I add a considerable amount of foam padding to achieve this, and also make certain that the bows are really secure.
• For players who only travel once or twice a year with their bass or tenor instruments I would suggest that they simply purchase a seat for the instrument. If you fly a lot, a quality flight travel case is a good investment.