A couple things:
1)For strong beers in their appropriate categories; I try to figure out what the likely category size is and the bigger the category the further I push the gravity/strength/ibus (if appropriate) on the contest beer. My theory is that judges get palate fatigue (well that's not theory, that's fact...but I digress) and therefore you need a more standout example of the style for them to be wowed. IPA, DIPA and Barleywines are prime categories for this. I don't personally like the idea of entering one beer into two categories by strategy, just doesn't work for my ethics is all. One beer, one entry is how I do it.
2)Take on the responsibility of transporting your beer yourself if at all possible. You simply can not trust anyone to take care of your beer the way you'll take care of your beer. If they'd let me be steward (no reputable contest WOULD let someone steward a category they're entered in) and pour it for the judges, I'd do that too.
3) Plan your competition schedule out in advance. If you're gung-ho to win certain competitions or medals, make sure you're brewing beer at times that have them in prime condition for the contests. Beers that are old or hurried usually don't win.