I have practiced meditation to help me stay calmer in my own life (and sometimes even do it at the airport when I see bad weather and flight delays for the day). I find focusing on a mantra or some other phrase is often easier than trying to calm my breathing or finding a quiet place.
It isn't always possible to have a nice, perfectly quiet and comfortable place when you need a bit of meditation respiration, so having something to focus on, whether it is the hum of an airplane engine, or repeating words in a low whisper, these are meditations that you can do during the air travel process.
I like the focused meditation how to that the About.com Guide to Stress Management put into words Practicing Focused Meditation: How To Clear Your Mind With Focus- it is easy to follow even if you haven't meditated before. Steps include - "Turn your attention to your chosen target, and take in the sensation it provides. Focus on the sound, smell, sight, etc. and simply experience what it has to offer. The idea is not to think about it, but simply to experience it, being fully present in the moment."
For myself, when I have a long travel day ahead, I often sit down for 10 minutes with a cup of tea the day before traveling, and I close my eyes and visualize the entire day - from checking in to arrival at my destination. Any obstacles that come up during the visualization, I try and move out of the way.
So for example, I arrive at the airport and see a huge line-up at security. I envision having plenty of time to get through and having my coat in my arms, and any metal objects in a bin, ready to be scanned. I try and go through the entire travel experience and for me it helps me prep for some of the aggravation of traveling.
When I am working at the airport, it is more about breathing techniques. If there is fog, or a downpour of freezing rain, I know there are likely to be some delays and cancellations involving flights I may be trying to get out. I breathe in through the nose for 2 seconds, hold for 2 seconds, release through the mouth for 2 seconds while dropping my shoulders as I breathe out. I repeat this, and increase the number of seconds one at a time until I am at breathing in for 8 seconds, holding for 8 seconds, and releasing for 8 seconds - by that point I am breathing diaphragmatically - taking in deep breaths, filling my stomach first, holding and giving my body a chance to relax. It only takes a few minutes of my day but it helps me cope with most of the disruptions that may hit.
The About.com Guide to Stress Management also has written a how to including a simple breathing technique to reduce stress using a Karate Breathing Meditation - How To Reduce Stress and Become More Centered With Simple Karate Breathing Meditation. From the how to: "This simple Karate meditation is fast, but powerful. It combines breathing, which has been shown to have significant effects on the mind, the body and one’s moods, with simple meditation, to help you become more physically relaxed and mentally centered."
Another travel de-stressor that often helps me in trying to fall asleep is I bring along a notebook with me and I write out lists - sometimes it's a to do list, sometimes it is a list of things that I am worried or stressed about. This is one of the ways I find I can let go, plus I have a record then to look back at. If it is a to do list, I have a plan of attack. If it is a list of worries, I take a look at it and try and come up with ways to tackle them.
Because air travel is so linked to a stressful experience, it is sometimes hard to stay calm and relaxed. It can be extremely tiring from jet lag, or feel invasive with all of the security screening, so having some simple stress-relieving options is a positive thing.