Mandrill supports a variety of ports and configurations.
Port 25 - Authentication required, no SSL
Port 587 - Authentication required, no SSL
Port 2525 - Authentication required, no SSL
STARTTLS is support on the above ports.
SSL is supported on the following ports:
Port 465, Authentication required, SSL required.
Your authentication credentials can be found in the Mandrill settings page within the section called SMTP & API Info
The SMTP server name is smtp.mandrillapp.com
You may need to experiment and figure out which port(s) you can reach, and then match your settings to the configuration supported by one of those ports.