I crossed the line from north to south at sea in 2007 on a research vessel. We had a big to-do about it. It was an all-day affair. Myself and maybe a dozen other Pollywogs became Shellbacks that day and got the certificates afterwards to prove it.
Festivities started the day before at mealtime, when every Pollywog had to stand up in the messdeck, before the entire crew, and sing a song. For the rest of that day and into the next, Pollywogs were obliged to do everything the shellbacks asked of us. Mostly stupid little chores and games.
The next day the real ceremony started after breakfast. We first were sprayed down with the fire hose while crawling around the deck. After that, we went before the Doctor (who prescribed a shot of soy sauce and tabasco to drink). We then were allowed to kiss the Baby’s Belly (a shellback AB’s beer gut covered in peanut butter).
Finally, we appeared before court of King Neptune (the oldest shellback crewmember, who’s wig was my best new mop) and had charges laid upon us by Davy Jones himself (the captain). Our punishment was to take three rolls in the Whale’s Belly (which was a tote full of seawater and galley scraps that had been stewing in the sun all week).
The vessel then stopped at the actual equator and we were allowed a swim call to wash the stink off of us from the Whale’s Belly.
All in all I’d say it was a pretty authentic ceremony.