That's great you were able to bring it as a carry-on. Gig-bag is a great idea for this!
For what it's worth, I found this tip (below) while searching on the topic.
Best Answer:* Tell the person at check-in that you would like to check your guitar at the gate. You'll carry it with you through security and everything. Once you get to your gate, an agent will tag it and you can just leave it right outside the door of the plane when you board (just like people do with strollers, wheelchairs, walkers, etc). It will go in an auxiliary baggage compartment and will be right there at the gate when you get off the plane. It won't go through any of that rough and tumble baggage processing.
I'm thinking, if you get as far as the boarding gate, don't ask for permission, just see if you can get away with bringing it as a carry-on. I guess the main thing is, do whatever you can to avoid having the guitar tossed in with the regular baggage since that guarantees rough handling.
Flying with a guitar really depends on the airline, how full the plane is, the size of the plane, etc. So anything I write may not apply in "your neck of the woods."
First, the guitar I travel with has a case that is 44" L x 17" W x 5.5" T. It will fit in the storage compartment of a 737 or larger with ample room to spare.
I travel with a backpack and my guitar as my carry-ons. Sometimes, I have to gate-check my guitar but most of the time I have been able to carry it on without any problems. A full flight is the most common reason a guitar needs to be gate checked. When you gate-check your guitar, the process is exactly as it is explained above. However, at this point, do not try and carry it on the plane. The reason they tag the guitar at the gate is to let the flight attendants know it needs to be gate checked. This is one reason you should have a good hard shell case. Another reason to have a good hard shell case is people pack two weeks of luggage in their carry-on's (I'm related to one) and sometimes use brute force to get the bin closed. If your guitar is in that bin, it is nice to know your guitar case is stronger than that person's carry-on luggage.
In general, be polite and as helpful as possible. Airline employees are usually nice to you if you are nice to them.
Guitars are fragile, lightweight, and expensive. Hard shell cases are big, heavy, and offer protection from impacts, temperature and humidity fluctuations, and most importantly, the things you can not think your guitar will need to be protected from. Gig bags are small, lightweight, and made out of the same material as my backpack. 99 times out of 100 a gig bag will probably work for most things. It is when that 100th time occurs that hardshell cases immediately pay for themselves.