Portugal's one of the easier places to do this, especially as you can tolerate a bit of cross-contamination. Most of the traditional food is naturally gluten-free anyway — grilled fish and seafood, piri-piri chicken, grilled meats, rice, potatoes, caldo verde (just check the sausage in it), and the salads. It's really the bread basket and anything battered or breaded you're swerving, plus watching for flour thickening in the odd stew.
For self-catering, Continente and Pingo Doce both have a "sem glúten" section, and Lidl's Portugal range is decent too — rice cakes, corn crackers, gluten-free pasta, that sort of thing. Fruit, eggs, cured ham, cheese and tinned fish are all easy fallbacks if a shop's free-from shelf is thin. Pastéis de nata are off the menu sadly, but a lot of the almond-based sweets you'll see are fine — worth asking.
The phrases to have ready are "sem glúten" and "tenho intolerância ao glúten". Staff in Cascais and Lisbon are used to it and most menus flag allergens now. Eating out, asking for things grilled rather than fried helps, since fryers get shared with breaded stuff. Have a lovely time.