Secure way to encrypt (not hash) passwords?

I'm building a system that for reasons I'll outline below, can't used hashed passwords, but I'd still like to encrypt them so that it's as hard as possible to crack them, in the (unlikely) event the DB does get compromised.

Basically, the reason I can't store them hashed is because they aren't authentication details for my system, they'll be used to log into external services, and because of that I'd need to store them in a reversible format so I can decrypt the authentication details and perform remote logins.

What would be the best way to approach this problem?