The main thing to remember when you're getting pressured is to stay cool; if you freak out you're more likely to make mistakes. Remember that when you are blocking properly the only thing that can hurt you is a throw or an unblockable. If you freakout and worry about breaking out of the pressure ASAP you'll miss little oppertunaties your opponent leaves for you to escape, and won't be able to read overheads or tickthrow setups as well as you normally would. If you get panicked your opponent will be able to trick you with frame traps or counter hit your pokes if you do so at a bad time. So above all else STAY CALM! Pretend you're Bruce Lee, count sheep, recite mantras, do whatever you need to do to stay cool and collected.
Observe your opponent's strings; does he do the same blockstring over and over? Does he tend to lead into his overheads using the same setup? Does he have a particular move he likes to do a tick throw off of? Does he like to mix in frame traps and try to get you to poke out? Watch his habits; see if you can get a good read on him.
If your opponent uses the same string, Instant Block the last hit and do a 623C (it's invincible for frames 1-21; but has lots of recovery so it's best to be ready to RC it). If your opponent is going to tick throw you toss out a 2A (you should be crouching anyways). If he's going for an overhead Block or Instant block it and punish if you have time. If he's doing a frame trap do nothing, just keep blocking (you can go for an IB here but it's risky). And if you're not sure what he's going to do, or you are not confident in how to counter him, the safest choice is to block.
Your opponent is not perfect, he will eventually make an error in pressure, learn to identify and exploit these opportunities, but beware of him mindgaming you with a feint if you have been to eager to escape through the match. As you continue to thwart his pressure he may start to feel agitated and become more obvious or sloppy with his strings and mixups, when this happens you can more easily breakout.
Well, that's about all the general advice I can give you about dealing with pressure; all of this comes from me watching vids and my personal experience with massive and long lasting pressure.
The Absolute key is to not panic.