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You can buy window screens in various sizes and types that attach to the window frames with Velcro or sticky tapes from LaRedoubte, Amazon.es (Amazon Spain), and probably other sources.

@gwalks

Also, I suggest that you consider renting a house in a village or small town, which will probably be even cheaper than some city center apartment. Then, your cats can roam safely outside. City centers are noisy, very expensive, crowded and everything costs more. You can easily get services and goods in a nearby town, if you rent a village house. The air is better, it's more tranquil, and you will most likely have fruit trees in the yard, where you can also grow vegetables. Taxis are not that expensive, if you don't have a car to use. Some places have buses to the next town, as does my village of only around 50 people.

"The hardest adjustment for us will be the lack of screens on windows."

How do you know there are no screens on the windows? 

It's not difficult

mosquiteira = mosquito net

Leroymerlin PT     

BricoDepot  PT

as in this link which may be blocked as it's a link

@Strontium

Link came through -- thanks. It looks like it will be a great resource.

Cats are pretty intelligent animals, so even without screens and windows are open they aren't going to jump if they are on a third floor.

BUT, fly nets are so easy to fit and even if you're not up to fitting them yourself there are companies that will do it for you. They will come and measure the window exactly.

I had friends that lived in a apartment and they put a mesh around their balcony, it wasn't because of the cats but to stop pigeons. 

I live on the 4th floor with a wrap around balcony in a smaller town in Portugal. I have an indoor-only cat. Once Spring rolls around, I want her to be able to stroll out onto the balcony at her leisure, so plan to get screens for the windows and netting for the balcony to not only keep her safe, but to keep the flies and mosquitos out. Thanks for all of the tips and confirming I'm on the right track with my plan!

I don't believe one of mine is bright enough to be safe. He thought he could walk on a second-floor railing (first floor in Portuguese). He's fallen once. That height was survivable for a 1-year-old cat, though he used one of his nine lives 😉. He still routinely jumps onto or across things in a way that scares me half to death. I'd love to share a balcony with them. If we do, it will be netted, and for sure, all windows will be screened. I love my darlings. I would be heartbroken if their naivete regarding the big wide world caused them to get injured. When I look at rentals, I pay attention to whether the balcony could be feasibly screened in. I like the solarium type, so they can still be used in colder weather, but they can be opened up wide in the summer to let the air in almost as much as a standard balcony.

I remember seeing one on the market years ago, in the Buarcos area adjacent to Figueira da Foz proper, where that area was glazed, which might make a lot of sense in that climate.  There was a terrific view out over the sea from that side.  Probably the windows could slide open depending on weather, don't remember.  Of course that's additional complexity, as you'd want one or the other but not both, but it would be a big asset during the winter.

(It was a house, though, not an apartment.  I'd edit my post, but the Edit option seems to be nonfunctional.)

(It was a house, though, not an apartment. I'd edit my post, but the Edit option seems to be nonfunctional.) - @donn25

Edit function only active for fixed time after you post then it's disabled.

OK, let me put that to the test.

Is the fixed time less than 15 seconds?  Edit doesn't work.