Well, it's a bit of a cliche in movies to split up but that's what so often happens. Sometimes the rationale is good ... such as if there isn't much time because a deadline is looming. Other times it's simply to make the characters more vulnerable. This sounds like a good idea in theory, but in RP, of course, your players will spend their time either in the action or waiting for the action so it's got its own pitfalls. Therefore, splitting up the party is an enemy of pacing but a possible friend of tension.
In a split party, be aware that the uninvolved players are likely to grow bored if too much time passes or frustrated if you flick back and forth too quickly. So what can you do to off-set this?
In some sessions, particularly if your players are good at separating meta-game knowledge, you can keep the tension and the interest high by having the players sit quietly and watch what happens to their friends while leaving them helpless to assist.
An alternative is to separate the players as well as the characters. If so, try to keep it short and tense and then bring them back together within half an hour. Any longer and they're bound to grow so distracted that all of the tension will dissipate unless you have very focused players. If you do this, you probably should have the other room be twice as atmospheric and keep them away from the television set. This can work particularly well for non-horror genres though some horror players will quite happily keep themselves anxious for the duration.
You could instead enlist a co-ST beforehand if you see it's going to come up. This is especially true if you're going to be the one to split the party. That way you can talk them through their side of the adventure.
If you don't have any advanced notice, you may be able to get another player to run a combat scene or something similar while you deal with the RP, traps, or room exploration. This can work out just fine for fantasy genres.
Sometimes, if one player decides to do a lone wolf and run off from the pack, you might be tempted to let the lone wolf play through their inevitable demise and let the other players bear silent witness. This can backfire as the player might either be resentful that you orchestrated their demise or dance through the spotlight and eagerly await another opportunity to do more of the same. If they're being poblematic, your best bet is to make their treks on their own incredibly dull. Have all of the encounters, drama, and excitement occur where the others are and have that individual have a remarkable easy and boring route to the end.
Do how do you deal with split parties?