One time I played a 4.0 player at a tournament. I thought the match was going to be in the evening, but the director left messages I didn't get. 8:30am the director calls me and tells me the match is at 9:30am. I had to bathe, gather my senses, and then get to the tournament. Add to that I'm a 3.5 player and I was thinking I am so screwed.
I played my opponent and the sun was just beating both of us as the match went on. We had numerous 30+ stroke rallies, neither guy seemed eager to serve hard, I hit quite a few solid backhands, and when all was said and done I lost 6-4 6-4. I wasn't even upset which was unusual. I actually felt like I had come quite a ways in improving elements of my game. Both sets went 4-4 where I got broken and the guy held.
Since that match as well as a few humbling losses and wins, my forehand has improved considerably (stuck with the extreme eastern grip, not trying to generate mad topspin so I can focus on generating pace hitting flatter, stepping into my shot more fluidly), the kick serve has become one of my first serve options (still can't trust it for 2nd serves), and I got some experience playing against other 4.0 players (got my butt whooped but I fought).
Another time was when I played a 4.5 player and lost 6-1 6-1. I broke his serve once and 7 of those games went to deuce. I felt lousy at first, but in reality I was not expecting to win and I did force him to hit some great shots.