My family came from Italy aboard the MS Saturnia in 1960, landing in New York. I cannot find any sort of passenger manifest or list from their voyage. In fact, the Saturnia page on the website jumps from 1959 directly to 1961, so I don't even have a voyage ID number! Would I have to contact immigration here in the US, or the Italian consulate in New York, or someone else entirely?

Try this one:

6182 Italian Line Saturnia New York, Boston, Halifax-Ponta Delgada, Lisbon, Casablanca, Gibraltar, Palma De Mallorca, Barcelona, Cannes, Genoa, Palermo, Naples, Patras, Venice, Trieste 1959/11/26 459

It took a couple weeks for the ship to arrive to it's destination so it may have left late 1959 and arrived in 1960. I checked the www.pier21.ca site as well (Halifax) and it was definitely the last voyage before 1961. BTW... my mother arrived on this same ship in 1961.

That seems right, but my mother is insisting that the trip happened in November 1960. But she says the other details are correct.

Ok well lets start with this then. Did she arrive in New York or through the Halifax Port? Because she is still alive, if she arrived at the Halifax port she may request a copy of her Ship Manifest from Pier 21. I have the paperwork around my office somewhere as I have been meaning to write away for my mother as well. I will let you know. I believe its a 30 dollar charge for the copy.

I, too, was a passenger on the SS Saturnia in November of 1960; and, I too, was hoping to find a passenger list. Unfortunately, I came accross the same problem of the 1960 records not being available for the Saturnia.
I do remember the following: I traveled with my mother and father. Although I was only four years old at the time, I do remember some details. We left from Napoli in November (I don't remember the date. I think we traveled for 10 or 11 days, though). I believe we landed in New York either on Thanksgiving Day (which was November 24 in 1960...at least so says the internet) or a date very close to that. I remember this because, I remember celebrating a special and unfamiliar holiday with our American relatives when we arrived.
I hope this helps. My plan is to continue to try to locate the November 1960 passenger list for the SS Saturnia. I ask anyone to please offer any suggestions. I welcome all suggestions. Thank you.