Sounds like a missing feature. Perhaps you should contact the company and make a feature request. :)
If the COM Server is local then you could probably call NtQuerySystemInformation
] with the SystemHandleInformation information class for enumerating all open file handles and matching it with a process ID. This may or may not work; it depends on the process keeping a persistent open file handle.
Another idea... would be to create a wrapper process that launches the COM server via CreateProcess
] and have the wrapper process export an interface for obtaining the process id.
If its a remote machine... out-of-proc via RPC then unfortunately you are out of luck.