I'll take advantage of your domain knowledge :) Where's the best place to find local artists that produce them?
In Spain, if you drive 1 h 20 minutes southwest of Madrid you get to Talavera de la Reina, which is a town all about ceramic and pottery:
I would love to help, but it's not my domain. I, unfortunately, witness the side-effects of people stealing them on my day to day. There are many shops in Lisbon that sell them, and there's even a beautiful museum here that it's definitely worth visiting (or signing up for a workshop!): https://museunacionaldoazulejo.gov.pt - it's currently closed for renovation; it should reopen later this year, but that's yet to be confirmed.
When buying - on the streets or in a shop - if it looks old, unless provenance is absolutely clear, please don't.
You will find great artista in Spain and Portugal. I can recommend you Talavera de la Reina in Toledo, Spain. It has a centuries old tradition of producing quality ceramics.
Viúva de Lamego is not a "local" artist per se but they're a leading artisanal workshop in classic and contemporary Portuguese tiles. If you have the budget, their tailor-made tiles are something else, imagination is the limit. (source: my dad does a lot of house restorations in Portugal and some require custom tiles to fill in missing/damaged areas)