The big difference between Sephardic and most other European genealogies is that Sephardic research is principally in archives rather than online databases.
There is no harm in looking at commercial databases like Ancestry.com, MyHeritage.com, free ones such as JewishGen and the Mormon FamilySearch or collaborative online family trees such as Geni, but it is in the archives that you will find the real treasure.
The resources listed below are principally those specifically focused on the Nação – either New Christians persecuted by the Inquisition or members of Spanish and Portuguese congregations. These include archives from:
In time, other countries and resources will be added.
A short-cut to finding relevant archives is to search in academic books and look at their footnotes. You can sometimes find references on the Internet including Google, Google Books and Google Scholar. I am fortunate to live in London and have one of the world’s greatest libraries on my doorstep. WorldCat indexes the collections of around 10,000 international libraries.
RAMBI is the index of article on Jewish Studies.
You need to be very careful when researching online. Many – perhaps most – of the online family trees contain errors. Anyone can claim to be an expert, and many do (have a look at the Myths about Sephardim page, to help sniff out the charlatans).
I find the Dictionary of Sephardic Surnames (Dicionário Sefaradi de Sobrenomes) by Guilherme Faiguenboim, Paulo Valadares, and Anna Rosa Campagnano to be a valuable tool. It is not cheap, but can probably be found in major libraries. The book is a meta-index of surnames names found in dozens of academic works on the Western Sephardim. Those books, in turn, reference the archival sources which can then be consulted.
Clearly there is no way of knowing if a name in a book is a family member, but finding the surname in the right area.