Portugal has one of the most complete historic archives in Europe. Much of the archive is held at the Arquivo Nacional Torre do Tombo in Lisbon (pictured above).
Portugal is digitising its national archives. One way to do a simple search for a family member is to go to http://digitarq.arquivos.pt/ and enter the family surname you are researching and two other words, for example:
processo judaismo Castro
You can refine the search by adding other words, or dates or by specifying you want only documents that have been digitised. There are other, more sophisticated, ways of searching, but this will get you started.
It is important to remember that only a few names will appear on this index search, whilst the Processo itself could contain hundreds of names.
The Torre do Tombo site is popular and can sometimes be very slow.
As well as the Torre do Tombo, Portugal’s regional archives are online. Here you may be able trace your ancestors’ baptisms, marriages and deaths through parish records for individual churches. (http://dglab.gov.pt/contactos-arquivos/). To be honest, this is not something I have yet done. Nobody has indexed the archives, and some of the parish priests had terrible handwriting.
I have yet to research in Portuguese notarial archives which are likely to be important for a community so involved in business. I don’t know where Wills are lodged. Possibly with the bishops’ diocesan courts, as in England.