I've done loads of reading and "giving medicine to relax" is most definitely a big NO-NO when animals fly. Reason for this is that because of the pressure difference and the altitude of the flight, the effects of any medication may be unpredictable and if the dog is sedated in any way whatsoever, it is difficult for the crew to determine if they are well or not. I don't know about herbal stuff like the ones you get from ECO - like ECO-FEAR, but very few airlines will, unless under direct and written supporting documentation from your registered vet, give any medicines to relax animals.
Sorry - I know we'd like them to sleep through the whole "ordeal", but that may just risk their lives and their future health very negatively.
I've ready somewhere else that good advice is to get your animals used to their travel boxes LONG BEFORE the flight - so get them as soon as you confirm everything and "play" around the travel boxes and in them with your animals often so that they can get used to the idea that the box is not a bad place to be.