Here's a quick mechanic I used during an M20 game played over the last couple weeks. Set in the 1790s, PCs were 0-Level servants in a New Orleans antebellum manor where their employer (to whom they were very loyal) was thought to be in danger. Their main objective was to investigate by speaking with guests and others to try to determine what was going on.
So rather than random encounters, I saddled them with "chore dice." Kind of like reverse resource dice, each occupation had a different one (Footmen were d8, as they mostly hang outside, while Butlers were d4 and always being asked about something).
At the outset, rolling a 1 meant PCs had to stop what they were doing and attend to some menial task (a great way to introduce red herrings, by the way). As the evening went on and became busier, a 1 or 2 would pull them away. I was thinking of having this work like resource dice in that rolling a 1 moved you down to the next smaller die, but for this game I found that simply increasing the target to 1-2 did the trick.
I wanted to toss this out here in case anyone required something to introduce tension without necessarily relying on combat or set encounters. It does mean you need to have a couple of ideas for these menial tasks. For the game last night this worked well to temporarily distract the PCs from their goals, sometimes for worse, sometimes even for better (their distraction leads them to some clue they wouldn't have otherwise found).