I would keep the COBOL core but expand around the edges.
Microfocus provide a tool called Enterprise Server which allows COBOL to interact with web services.
If you have a COBOL program A and another COBOL program B and A calls B via the interface section, the tool allows you to expose B's interface section as a web service.
For program A, you then generate a client proxy and A can now call B via a web service.
Of course, because B now has a web service any other type of program (command line, Windows application, Java, ASP etc.) can now also call it.
Also, they have a product called COBOL.NET which runs inside Visual Studio and translates COBOL to MSIL. This means that you can then link in any .NET components.
So the approach is to keep the COBOL core but interface via web services and do new developments in any CLR compliant language (C#, VB etc.)