dishonored
So I'd decided to go non-lethal on this mission. I figured out who Lady Boyle was by reading notes in the ladies' bedrooms, went to tell her someone wanted to talk to her in the wine cellar, followed her there, and sleep-darted her.
Now I am stuck with a sleeping Lady in the basement. No new objective has appeared.
What did I miss ?
Are you talking about this one:
(Image from the Dishonored Maps App for iOS.)
If so, doesn't look like there's anything of note there. I don't recall finding anything interesting.
If anyone sees you while you're trespassing (upstairs) everyone will turn hostile (one person seeing you = everyone, oddly enough), I'd bet that's what's happening. It can be tricky to come back downstairs without being spotted (even when using tricks like timestop and blink people seem to see me). Note that you can totally kill/knock out the upstairs guards without alerting everyone else if you're careful; every playthrough I've done I've KOed or killed the guards upstairs and I usually get out scott-free.
Try exiting the downstairs via a more discrete way: you can leave via the balcony (the door to the outside from the first bedroom after the stairs) and the guard outside won't "detect" you (he's also easy to knock out or kill, but it's pretty unnecessary). He just politely asks you to stop trespassing. Drop gracefully from the balcony and no one should turn hostile (note that falling on someone's head, as I did the first time, counts as an attack).
Also note the basement, oddly, doesn't count as trespassing, so I'd poke around all the "safe" areas before going upstairs, and making a real save before going upstairs, since it's usually when things go south in this mission.
Best Answer
To non-lethally remove Lady Boyle, you need to help Lord Brisby abduct her. Speak to Brisby (he's the one in the hideous mask) and he'll tell you he's in love with her and to bring her to him in the cellar (which will add his location as an objective).
Identify the correct sister and bring her unconscious body to him. Luring her to the basement is optional but makes this much easier.
Dishonored is quite robust when it comes to doing things in the wrong order- speaking to Brisby then giving him the already unconscious Boyle should work. If not, you will need to load an earlier save.