Does any aspect of the sotah procedure still hold effect today? For example if a man tells his wife, in front of 2 witnesses, not to be secluded with another man, and she secludes with that man for the amount of time it would take to have relations, is she forbidden to her husband?
Yes it still applies. The laws are found in Shulchan Arukh EH 178.
Do not ever do a proper Kinui (warning not to be secluded with X) to your wife, even without witnesses, because if she ends up alone with the other guy, even by accident, you must get a divorce as there is no Sotah-water. It's just not worth it. Have a heart-to-heart talk instead.