If I can get away with it, I have the PC in question be absent, and try to work out something one-on-one with them during the week.
If not, I run the PC as an NPC (or have the players do this). Although, the only time I can remember doing that, it was on a session that was going to begin with the BBEG fight (there wasn't quite enough time at the end of the previous session) and several players didn't show up. So I had the two remaining players run their PCs. Sadly, it was a bit too tough of a fight, and two PCs died, one belonging to an absent player. That was a fun phone call:
"Oh, BTW, you need to roll up a new PC. Your druid died last session."
"Why were you playing my character?"
"Because we sort of left off at a cliffhanger and I couldn't just poof you out or have the other two guys just 'do something else'."