Is there any way that a Silverlight out-of-browser app can communicate with another app (for example an Objective-C app) installed on a Mac?
Any help or suggestion will be highly appreciated.
If what you mean by "a Silverlight out-of-browser app" and "another app (for example an Objective-C app) installed on a Mac" are simply two processes, and you're looking for an interprocess communication mechanism, there are several possibilities.
Since Silverlight has both a networking (sockets) API and a filesystem API, those should both be good options. I'd probably use TCP/IP networking, which I'd expect to be pretty fast when both processes are on the same machine.