How big a shield are we talking? If you are talking about the ever-prevalent tower shield then you are looking at a hard fight no matter what. However, there are some techniques that might work depending on your style and what handed fighter you are.
For instance: Sword and board concentrate on moving into your opponents sword arm with your shield and coming around the side of their shield for a shoulder attack.
Dual Wield block an incoming attack with your off hand weapon and continue to put pressure on it. If he takes pressure off his own weapon it will allow your off hand to make a hit. If your opponent continues his pressure as well, attack the arm at about the elbow.
Large Red focus on weapon side then come around with a large hit to the bottom of the shield. Two of these and he has no shield and you have a reach advantage.
Single Blue block sword arm with weapon then grab his wrist with your off hand. Pull him off balance and deliver an attack to the back. This of course is assuming that you are not wearing armor since you cannot innitiate a grapple if you wear armor.
There can be any number of ways, but like Aodhfin said, most of them concentrate on doing something with the "weaker" side being the weapon arm.