I used Wireshark to capture a connection of the UC Client and ucCompannion
UC Client info:
Looks like it uses a source port of 54269 and a destination port of 5746
Source port of 54273 and a destination port of 7777
Hope that helps. That is all I saw regarding communication from the client to the server.
For UC in general, these are the typical ports in use. Keep in mind the client requesting (SRC port) could be anything, i.e. 54xxx and up.
ucCompanion Live Attendant
SIP Phone Discovery adapter
Proxy Port - SIP PBX
Services (MOH, queuing, park/pickup, conferencing)
Generic PBX via Gateway - 3rd Party PBX Integration
Application Server - VM, IVR, PA, PBA, + others where additional PBXs are required