The Sharks got a very soft return for him after a Norris winning season, that was with retention and facilitating Pittsburgh dumping multiple negative-value contracts. (Yes, the pick ended up being fantastic - but at the time it was projected to be in the 20s and San Jose had to give up a pick projected to be in the 60s to get it.)
I doubt there would be a market for him at the deadline, unless there are serious cap considerations. At that point, Pittsburgh maybe gets a few B and C pieces, with the primary asset being whatever cap they clear.
They might get lucky in the summer with the cap potentially going up near 100 million. If a team strikes out on some RHD, and Pittsburgh is willing to retain 25-50 percent, it might make sense to take him.
You have to keep in mind that he is 35 in may and has an extensive injury history. If he only had 1 year left after this one, he is a lot easier to move. Teams are going to be very reticent about taking on a contract that will have that second year remaining, is completely buyout proof and also has a NMC. Add in the fact that they have to give up assets to Pittsburgh, and Karlsson has to agree to waive. It could make a trade very complicated.
Karlsson also probably figured out by now that the grass always isn't greener. He went to San Jose and they ended up in a rebuild. He want to Pittsburgh and they ended up in a rebuild. So long as Crosby is around, there is always a chance for Pittsburgh to sneak into the playoffs. They were supposed to be rebuilding right now and they were still in it up until last week (and they could still bounce back). Accepting a trade to another team that isn't a legit top 3-5 team in the league doesn't guarantee him anything in terms of playoffs, and he has to go through the hassle of moving again when he is probably 2 years away from retirement.
Montreal makes the most sense to me. They aren't a contender, but they are a 2 hour drive or 30 minute flight away from Ottawa, which is Karlsson's adopted hometown still. So it is logical to assume Karlsson might waive to go there. They have a few bad contracts with term like Josh Anderson that Pittsburgh could take to offset the cap hit of Karlsson. They also have a history buying low on bad contracts of skilled players (Monahan, Laine). Josh Anderson for Karlsson with some retention would be what I would expect. Then Pittsburgh can buyout Anderson in the offseason (Karlsson is buyout proof). Effectively, they would get out of a large chunk of the Karlsson contract.
With Alfredsson being on Ottawa's coaching staff, and Ottawa recently striking out on Klingberg, it obviously makes me wonder if they would try to get Karlsson back. With the team rallying, I think it would be a risky move. Karlsson only existed in Ottawa as the face of the franchise. Coming back to a team with a new core and completely different norms than when it was his team might be disruptive for everybody. A trade to the Senators would be difficult, because unless they do Norris for Karlsson (with retention), Pittsburgh likely has to retain close to half while also taking Perron and/or Amadio.
I don't think Pittsburgh gets much back for him, but at the end of the day, cap space is an asset and owners dont like spending significant money on players during rebuilds. If it comes down to dumping 50-75 percent of Karlsson's money but getting very little back in the way of picks or prospects, I could see them still doing it. They aren't going to get value by keeping him around if they are intent on tearing down the team.