It’s possible to upgrade for a single journey, but I wouldn’t call it a special offer and it’s not for free. It’s really expensive (116 CHF per person if doing the whole trip from Zermatt to St. Moritz).

There are cheaper ways to do this if booking long enough in advance. Maybe it’s even a better idea to buy a 1st class railpass as you’d have 1st class on every train not just on one.

Otherwise, it may also be cheaper not to use your pass and to buy a swiss day ticket (does start at 88 CHF 1st class two month before a specific travel date).  

(Regarding your other post: If you’d like to go just to Switzerland and do a single trip to Berlin, then a Eurail pass may not be the best idea; if you are doing some other trips, it will.)

The Swiss Railways do offer saver day tickets that may be another alternative if you want to travel in 1st class (I’ve been on the glacier express in 2nd class and it’s still pretty good, but understand if you are 2 people maybe you dont want to share a table). 

These would be valid on that train once you pay the reservation supplement as with a Eurail or Interrail pass. 

The Saver Day Ticket ranges from around 88-170chf per person in 1st class, without the Swiss half price card.  You can check the days and prices here; 

https://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/day-pass/saver-day-pass.html 

Andrew

There is no free upgrade with Eurail. 

thank you!!!