Visual COBOL allows you to deploy COBOL applications as SOAP or REST web services running in Enterprise Server. You can also generate COBOL client programs that are capable of calling these or 3rd party deployed web services.

There are a couple of videos that describe this feature in detail:

Using Visual COBOL for Eclipse to Create SOAP Web Services

Using Visual COBOL for Eclipse to Create REST Web Services

There are also a couple tutorials in the product documentation that will walk you through this process.

Web Service Tutorials for Eclipse

Web Service Tutorials for Visual Studio