cell phones

A few years I was in your position with an older phone bought in U.K. and really needed a phone at the airport had used a TIM sim previously. Tried to buy same at airport told could not do that any more
and was sold acompletely useless overpriced new one. A few days later went to Tim shop bought a SIM card with credit for about 20 euros and used it for two months topping up as needed by helpful Tim staff who very kindly organised English on phone as I very
techniclly challanged. I had previously used Tim for 8 months while living in Tuscany. Motto :- don't be caught out at the airport.
Vogue Australian

If you happen to be a Sprint customer you should look into Sprint's "Global Roaming" plan. It costs nothing to use the plan, offers reduced rate phone calls, free 2G data and free texts. Global Roaming worked well for us in Britain last year. Take a look here for more info:
https://www.sprint.com/landings/international-value-roaming/index.html?ECID=vanity:globalroaming
Other cell phone service providers may offer similar plans.

SIM cards are usually in "all sizes", you pop out the correct sized piece of plastic from the card. Cell phones use the same standard all over Europe, so that shouldn't be an issue (unlike US phones that can use different standards).
But, there are 2 possible issues:
1) Is the phone unlocked? If not, it will only work with SIM cards from the company you bought it off. You may be able to get it unlocked at a phone shop.
2) If you bought it in the UK, it will have a UK plug on the charger. You then need a UK/Italian plug adapter (not a US/Italian one) in order to charge it up. Or a different charger.

Thanks for such helpful advise, especially about watching out for being scammed. The phones are unlocked and I do have all the needed adapters; the issue is whether I can still get a SIM card for my old phone.