happy to share gluten free resturant/food search. my wife Carol eats gluten free and dairy free by choice not a celiac sufferer. Italy does have the AIC which will certify a gluten free resturant and some gf resturants will have that displayed in their particular websites and or in their establishments. i also printed off and a free, gluten free card in french and italian which is specific to celiacs and edited it to fit carol's choice so that if we were not clear then we could use the card with waitstaff and be understood. the card is done in the language of choice and translated into english as well. very easy. for a celiac you would want the card printed as is.
i broke up resturant searches by area visited. rome pretty easy, florence less choice but doable. we know carol can fall back on "clean" food choices basic grilled/roasted meat/fish and basic vegs and salads. made sure to alert olivia on the dietary request of gf and df and will repeat on board ship. the search was pretty simple using google. search "gluten free rome",same with florence and of course anywhere else. the smaller cities we go to not much choice and we did not need to hunt. also used google maps and located our hotel and tour areas to search "gluten free resturants near ---". you will see a number of them. some just pizza and other full on resturants, gelato places etc.. using gf as first words in search is best then pick through the results in articles for the areas.
here are a few in rome: http://www.mangiafuoco.org, http://www.mamaeat.com,http://www.pantharei.it
there are more i was well served using google translate and reading further into menus on some. trip adviser and google had reviews locations and all particulars. hope this helped and happy hunting. also make sure if breakfast included in your hotel that they have gf choices ex cereal, bread for you if needed. italian stores do have such choices available.