Last week on Liberty we arrived later than we normally do. It was around 1:00p.m. and the lines were actually shorter than what we've experienced, in our last few cruises, when arriving at 11:00 or 11:30 a.m..
I have to say that I really didn't like all the "kiosks" in the check-in area. Go here and drop off form. Go there and scan passports for check-in and get ticket. Go to another line and hand ticket to agent and receive Sign and Sail then go around and get on ship. I know the automation saves check-in personnel but it was somewhat confusing for many people.
One tip for embarkation. Bring a small carry-on with just the necessary items. You will have to lug it around until the cabins open up.