In my last job we wrote a front-end that ran the COBOL and streamed the presentation information to the client over a websocket. It allowed them to use 30+mil LOC of existing apps.

The resulting webapps were made automatically responsive for the web and could be run anywhere - desktop, tablets, phones and apps could open tabs that invoked other apps for multitasking. We also added some custom commands to the COBOL so that they could invoke web based graphs, reporting, printing, pdf generation, etc. The client supported native typeahead, so the web apps behaved very much like desktop apps whereby pressing a number of shortcuts simultaneously resulted in them being played in order and overcoming any latency. This made the apps completely superior to normal web apps for their application (i.e. POS, ERP systems).

The utility that COBOL provided, coupled with a modern web based runtime written in React, was remarkable. Truly a hybrid of both the best parts. When I left, they were working on wrapping the React webapp into a React Native app.