Some professional organisations provide "lifetime" email aliases - for example, for physicists the Institute of Physics provides physics.org addresses. That's the solution I've been using for two decades now. The alias can be set to forward to whatever address you want. I think this also looks more professional/authoritative than a consumer webmail address. Note though that it's a long time since I checked the T's & C's; keeping this service might depend on paying the IoP subscription.
Answers to What email to use for corresponding author on publications when institution is not permanent? and E-mail address to use in publications also mention the ACM (computing), AMS (maths) and IEEE (electrical & electronic engineering) as providing such e-mail redirectors. I prefer this option to, say, Gmail as it suggests a long-term commitment to the field on your part, whereas a Gmail address can be disposable (indeed, I associate Gmail with throwaway addresses used by spammers).
Contrary to what some have said: my experience is that you can't trust institutions, especially after you leave. My last university randomly locked my email access without warning, wouldn't set up forwarding, and hasn't passed on snail mail either. (And by the time you find out they're a bad 'un, it's too late.)
The other option is a unique identifier, such as OrcID, though quite how they will pan out in reality remains to be seen. Bear in mind that even if the OrcID organisation disappeared overnight, a web search for the identifier will still come up with material that includes your contact details, so it's worth embedding it in your (relevant) social media profiles.