Production level servers can be tricky. Mostly because of the inherent, increased security needed to protect online (and exposed?) assets. Our Postgres server is one such asset.
But opening the necessary ports to allow access to the database server (for maintenance) can expose the server to possible attack. Fortunately, if your Postgres server is on a UNIX or Linux based machine with SSH installed, you can forward the Postgres port through the SSH tunnel.
ssh -L 1234:localhost:5432 firstname.lastname@example.org
In PGAdmin, simply connect to localhost:1234, and you will connect to the production server through the SSH connection without the need to open a port on the external firewall.