The syntax in the Instance field of the Database Connections tab to connect to an Oracle database listening on a non-1521 port using EZCONNECT syntax with ArcFM Geodatabase Manager is:
Matthew St John advised:
I've gotten back some info on the connection string format. We have in our Appendix information on a longer connection string format which is normally not used, but which appears to be necessary for the fully-descriptive format needed to do a direct connection to a non-1521-hosted Oracle service:
This connects to the server Minerva on port 1522, with the EZConnect name "orca10.minerva". Under normal circumstances the "/;LOCAL=" part isn't necessary, but for this port setting it is.