If you want to chase a flush or straight, you need to be willing to bluff at least some of the time when you miss. Otherwise you will have a hard time getting enough implied odds when you hit to make up for the vast majority of the time that you do not.
This is basic advice but I notice very few players, even at high stakes MTTs, who seem to do this with any consistency. Some try to hit their draw cheaply, betting 1bb per street until they get there. Others will play it aggressively, either as a check raise to blow someone off a pair or just by leading pot on the flop and turn. But in either case, you see a LOT of check-give-up on the river when the obvious draw doesn’t come in.
That is a LOT of chips you are handing to your opponent! Especially for those on the aggro side of the aisle: imagine a single-raise pot, betting pot on the flop and turn. In many cases you have put in over 1/3 of your stack by the river… and now you are just going to check and fold to a bet? This is a killer for your tournament prospects, and it will happen 2/3 of the time or so on most draws.
Think about what kinds of rivers you can credibly represent with your line. If you sense your opponent is hanging on with 1pr, consider overbetting the river. Have you ever faced an overbet on the river, staring down a wet board with just top pair? It is not fun! 
But whatever you do, don’t just automatically/always check-fold when your draws miss. If you aren’t comfortable occasionally bluffing the river, you should probably just play fewer draws, or only the more disguised ones (backdoor flush, double-gutted straights for example) so that you’re more likely to reap your implied odds when you hit. Without this element of strategy, chasing draws is probably just -EV in the long run.