I'd be intersted in a response to this too, as recently I had to take my cat to the vets and it cost me 180 euro! I think they kind of saw me coming and they still wanted to do additional tests (more money!) once my cat was well again. I asked at the time about Insurance but no one seemed to know what I was talking about. I have found sites that cover pets in Spain so possibly there is something similar in the Algarve..purely guess work but it seems to me that what is in touristic Spain is normally in the Algarve only (that is for ex-pats anyway). It does seem to me though that pet insurance is not yet available here.
My dogs are insured with Villas-Boas ACP but the insurers seem to be called Fidelidade Mundial and I pay €82.40 a year for two dogs, the third was too old. BUT they are mongrels which interested me as I thought that it might only have been possible for pure breds. They are a bit slow but it works. Not, however for routine visits or vaccines, but for specific health problems it does work. I have also seen that Millenium bcp -even with all their current problems! - seem to be doing pet insurance called Pétis from 5,04€/month www.millenniumbcp.pt or call 707502424.
I forgot to put the address of Villas-Boas who are the brokers for Fidelidade. It is www.villasboas.pt te. 213236000 or email: geral@villasboas.pt.
Hope all that helps as I know vet's bills are horrific.