After a game of Boggle, players usually have a list of question-marked words -- things they're not sure about but wrote down just in case. Rather than look up all of these words in the dictionary to see if they're valid, I suggest the following improvement:
First, any question-mark you have that
your opponent also wrote down (whether question-marked or not) is crossed off.
As for the remaining ones, you can look them all up in any order you please, but ONLY as long as each one turns out to really be in the dictionary. Once you try a word that's not in the dictionary, that's it. You can no longer look up any more words, and your remaining questionmarks are thrown out (except for ones your opponent graciously admits are valid).
This rule adds strategy to the scoring part of the game, as you will have to look up your words in order of confidence, and even account for the potential value of the word should it be valid. For example, suppose you're down by 3 points after the main word lists have been compared, but you have the following question marks: SUD, RESITE, FOW, UZI, HIN. Even if you're least confident about "Resite", you may choose to look it up since it's worth 4 points if valid. Otherwise you'd need all four of "Sud", "Fow", "Uzi", and "Hin" to be valid, and if one fails you no longer get to try "Resite".
This question-mark rule also puts a limit on the amount of nonsense that players will write down, as it becomes unlikely that they will even get to look up all their questionmarks.
If both players have questionmarks to look up, this can be handled either by having the players take turns looking up one word each, or whoever's behind after the main word list can go last, or the original shaker can go last.
P.S. any of your words that your opponent "challenges" while you're reading your main list become automatic question marks. You can get them back by proving they're in the dictionary, but they follow the same rules as the other question marks. If you're really so confident it's a word, look it up first!