My current compromise:
When using two weapons, roll your attack as normal. If you succeed, roll the damage of each weapon. Keep the highest.
This gives a slight bonus without being ridiculously better than a two-handed weapon or shield. I'd like to incentivize using smaller weapons with this - or at least, using something like "Sword and dagger" rather than "I'm duel-wielding longswords." I'd prefer to do it without having to resort to some kind of "one weapon has to be shorter than the other" kind of rule.