What happens if I miss my train connection?

I don't know if the train from sestri Lenvante is a Regionale or an IC. You can probabably proceed on the next Regionale, but if it is an IC train, it has a seat reservation with it. Regardless, you will definitely need one for the Milan - Venice leg. If it is Trenitalia's fault, then it should be free.

I would get on an earlier train from Vernazza to Sestri Levante since it is a regional train that takes only 36 minutes

I love mysteries. How did you get this routing? I am looking at 4 departures from Vernazza at 10:34, 12:34, 14:34, 16:34. These are Regionali that connect to IC trains to Milan all at the same times past the hour. Each of these Regionali stop in Levanto 10 minutes after leaving Vernazza, at 44 past the hour. They have an 18 minute connection to the IC train going from La Spezia to Milano Centrale. But you are staying on the Regionale all the way to Sestri Levante making each stop along the way. The IC train is nonstop from Levanto to Sestri Levante. Therefor it is almost catching up to the Regionale at Sestri Levante, leaving only 5 minutes to make the connection.

The way you are doing it might save a couple of nickels, because Regionali cost less per km than IC trains. Even though it is there at Levanto, you are not allowed to make the change there, as the IC train has a seat reservation and that does not start until you reach Sestri Levante.

Let me just say that I don't think the IC will catch you on the way to Sestri Levante. Just know that your connecting train is right behind you when you get to Sestri Levante and be prepared to get off the train before everybody else. The Regionale terminates at Sestri Levante and everybody is getting off the train. You will probably have to change platforms to get the IC train.

I love mysteries. How did you get this routing?

Me too, I suspect a re-seller's site (pushing tickets after the summer timetable change on June 10) or a travel agent.

My favorite routing is a regionale to Monterosso, then a direct IC to Milan followed by an high speed train from Milan to Venice.

If you miss a connection because of trenitalia, you are always protected. When travelling on trains with reserved seats (IC and Freccias) you must get a new reservation for free at the counter.

You might stop at a Trenitalia desk and see if they will let you buy a supplemental seat reservation for the IC train from Levanto to Sestri Levante. Should cost 3 EUR if they will let you do it. Then you can make a relaxed train change at Levanto.

I would just make the observation that "at the counter" can involve long waits in line, especially during the peak summer season. While I normally agree that command of Italian is not necessary for a pleasant visit to Italy, the window employees (especially at a non-major city) cannot be expected to be fluent in English. I would have all your documents at hand, so that your situation is obvious to a rail employee who is familiar with that type of document.

I would also write in the margin the actual arrival time of your late train ("Arrivato 14:23") or whatever, so that the problem is more obvious without good command of Italian.

If you did buy through a third party, how about emailing them with your entirely reasonable question, and telling us how their service was?

Regarding “mysteries”, I booked this online at the Trenitalia website a month or two ago, and there were no other options better than this one given for departure in morning time. I specifically avoided any reseller websites.
So, if there were better options why didn’t they offer them to me?

Thanks for the information and suggestions, everyone. Unfortunately, I guess the Trenitalia website just showed me the least expensive options, and the site didn't show other options to me with better (more than 5 minute) connection times. I wrote to Trenitalia and expressed my concern about the 5 minute connection, and they quite nicely responded, but said not to worry, the Sestri Levante station is small and there should be no problem for the connection. I think we'll just be sure to get off the train first in line, and find our connection train as quickly as we can...

Instead of brow beating you about your route, I will try to answer your question. Five minutes between is more than adequate. May not even involve a platform change. If the train is late and you are transferring to a train with a seat reservation requirement - non Regionale train, then go to the ticket window and they will issue a new ticket on the next train since it was their fault and they will know that the train was late. If you miss because you are seating in the water closet, then you buy a new ticket. If it is an open Regionale train ticket - no seat reservation - then you can jump the next Regionale train going in the correct direction. Five, ten minutes connections are very common.