EchoMac requires that UDP traffic to ports 5198 and 5199 reach your Mac. If you are using a typical consumer router that does Network Address Translation (NAT), you need to configure it to make sure those packets are forwarded from your global address to the address of your Mac.
If your router supports "port triggering" that can be the easiest way to get set up. The router watches for EchoMac (or Echolink) to make the connection to get the station lists (your Mac makes a TCP connection to the server on port 5200) and then automatically configures UDP traffic on ports 5198 and 5199 to forward to that address. This is particularly handy if you use different computers on your LAN (at different times) to access the Echolink network.
Slater, VE5OA, provided this screenshot of the configuration he uses with a DLink DI-624 router:
The Airport series does not support port triggering, so you need to manually configure it to forward to your Mac's IP address.
Steve, VA3SPH, provided these instructions and screenshots:
In Airport Utility go to Advanced icon, Select Port mapping, Click the + sign to add a portmapping and name it. I called mine EchoLink.
Add Public UDP ports 5198, 5199. Put the IP address of your machine where it says Private IP Address. Then add 5198, 5199 to the Private UDP Ports field.
Note: If using DHCP and you have a number of computers in the house. You may which to set a static IP address on your machine so that this rule for port forward always works. If another computer grabs your IP address then it will stop working.