For everyday documents, a qualified electronic signature does the job. It carries the same legal value as a handwritten signature across the EU. If you have a Portuguese residence card, you may already have this through the Chave Móvel Digital and not know it.
For documents that need more weight, banks, some contracts, official processes, there is signature recognition at a Portuguese consulate. You sign in person at the consulate in your country and the signature is recognised for use in Portugal. Slower, but solid.
For property deals and anything requiring a notarial act, the real instrument is a power of attorney. You grant specific powers to someone you trust, a lawyer usually, and they sign in Portugal on your behalf. Done properly, entire property purchases happen this way, from reservation to keys, without you boarding a plane.
Two things people get wrong with powers of attorney. They make them too broad, granting general powers when one specific act was needed. And they forget them. A power of attorney does not expire on its own just because the deal closed. Grant narrow, revoke when done.
The wrong answer, which I still see: signing at home, scanning it and hoping. For anything that matters, a scan of a signature is the weakest version of every option above.