One thing you need to be familiar with though. British Airways and others have different policies on rifles and ammo. BA required me to call them ahead of time and let them know about the rifles or they would not transport them. All American and Delta require you to declare the firearm when you show up and show your documentation before they check the rifle.
Also, for you Americans, we were going to take a rifle to Romania to hunt last year and filled out all of the paperwork both here with US Customs and with Romanian officials. I called BA ahead of the flight and made arrangements for that too (costs extra). Right before leaving, I noticed that the Romanian official had made a mistake on my permit and the SN on it did not match my SN on my gun. As it was too late to do anything about that in Romania, we decided to just used the George Dumitri's rifles there. This worked out OK in field as they had great rifles to use there.
Our problem came when we were leaving DFW to fly to Europe, a Homeland Security agent found us (randomly in the airport, as we were just walking through it to the gate) and asked us to come with him. He even had a BOLO sheet with our photos on it! My wife and I were taken into a small room with four homeland security officers and they proceeded to quiz us on why we did not have the rifle when we arrived at the airport.
Fortunately, I still had all of my paperwork on me in my "hunting" file. The agents went over my paperwork, made copies and after finishing the 30-minute grilling and us explaining what happened to them, they let us go back to the gate where our flight was finishing boarding procedures. Moral to the story: make sure you keep paperwork with you if you decide at first to take a rifle and then later change mind not to travel with a firearm.