Theres two things that will happen I find, either you stop eating , stand up and walk about burping a lot and make your way to the toilet ....If I try and sip when something is properly stuck that usually just makes me sicker as it has nowhere to go.
If it can't filter down I'm afraid it just comes back out rather forcefully (in my experience)
Or if you're lucky, waiting for a bit you can actually feel it slowly go down through the band....wait a few minutes and decide if you want to continue eating (talking about something sticking as opposed to having restriction when enough has been eaten btw) and also have a few sips of drink to make sure it's gone through the band.
Usually after getting something badly stuck which leads to throwing up the food, I have liquids or soft foods carefully for the rest of the day as it always gets aggrivated in there and I have learnt if I try and keep eating denser food after, the sickness and blocked sensation keeps with me all day.