My girlfriend and I were travelling to LA via Vancouver, we had our ESTA already from traveling earlier in the year, but had no idea about the Canadian ETA (completely our fault). Anyway, applied the day before, my girlfriends being accepted within 10 minutes, but I had to complete additional forms due to my military service (going by the questions asked).
To cut a long story short we were not able to board due to my application not having been processed, but the staff at the gate were superb, they phoned through to whoever in Canada, chased it up, and it came through within 45 minutes. Although we missed our original flight, they booked us on another just over an hour later, free of charge, and had already removed our luggage from the hold.
I can't remember all of the staff members names, but one I can was named Andrea, she was so accommodating and understanding. My girlfriend did run along to the shop to buy them some sweets to say thank you.
Thanks to everyone who helped, and we will definitely be flying with you guys again