I'm so used to testing connectivity to an ESXi server from a windows or Linux system, that I never thought about how to do it the other way around. It took me a bit to find it so I figure I should post on this for my reference @ a later date.
The key command from the CLI:
nc (aka netcat)
nc -z DestinationIP DestinationPort
In my case, I was trying to get Emulex onecommand to download and install firmware to my HBA's. Emulex onecommand was running on my tools server on ports 8080 and 8443. To test my connection, I passed the following command:
nc -z myToolsServerIP 8080
nc -z myToolsServerIP 8443
The commands would just hang, meaning the ports were not responding. A quick e-mail to my firewall teams and they were able to fix the problem by opening up the ports.
VMware KB: 2020669