Delaying the activation of Undying Rage is a very effective way to make an enemy champion over-commit to trying to kill you.
Bloodlust is an excellent way to heal Tryndamere. Try not to let it fade off before you activate it.
If the enemy is stacking Armor, try building items like Last Whisper or Youmuu's Ghostblade.
Try harassing Tryndamere early so he can't kill minions and heal with Bloodlust.
Remember, Tryndamere can only slow you if you are facing away from him.
Most of Tryndamere's damage is physical. If he's getting too strong, consider buying a Thornmail.