This question was answered by @vincro:

in the “Connection” panel:
Address - localhost
Port - 27017

in the “SSH” panel:
Address - <your_ip_or_fqdn>:22
and use a private key auth.

This will connect via port 22 and redirect traffic sent to port 27017

Mongo on your droplet is set to respond only to traffic from localhost which is where the ssh tunnel comes in handy. Running db.serverCmdLineOpts() from the mongoshell will tell you what it is bound to.

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Here’s the robomongo (v 1.0.0) setup:

Connection tab

• Address: localhost
• Port: 27017

Authentication tab

• “Perform Authentication” is turned off

Advanced tab

• Default Database is left blank

SSL tab

• “Use SSL Protocol” is not checked

SSH tab

• “Use SSH tunnel” is checked
• “SSH Address” first field is my server’s IP address, second field is the port “22” as was default
• “SSH User Name”: your private key enabled user
• “SSH Auth Method”: Set to Private Key
• “Private Key”: Click the … button to select your file
• “Passphrase”: left blank or filled as you prefer

Beware that the private key should be in OpenSSH format. If it is the case you may convert a putty key (ppk) with the “Putty Gen” app.

Additional details and tips here.

You can use ssh tunnel:

ssh -p <sshport> username@sshhost -L 27017:127.0.0.1:27017

That’s if you use the default 27017 port,