Assuming an IBM environment.... Having supported MVS/CICS for the first half of my career, and NT servers for the second half, I would recommend a complete rewrite of the application.
There are conversion tools like this, but I don't know how well they work.
https://www.ispirer.com/application-conversion/cobol-to-cs-conversion
I would think that a lot would depend on what data the program processes. If you've got a "batch" program the processes flat files or DB2 databases, those might translate ok. But if you've got "online" apps like IMS/DC or CICS, those are completely different animals and are typically dependent on the model of the 3270 terminal device that the user is using.
Have you ever heard the phrase "spaghetti code"? That is what we call COBOL programs that have been around for a while and where multiple programmers have made modifications over the years. The code typically has many GOTO's, paragraph names, PERFORM THRU's, and trying to make even a simple change can be a challenge trying to figure out the execution path. I can't imagine what the C# code would look like after being processed by a translator.
Micro Focus claims that it can compile to Dot Net. That might your best bet where you leave the COBOL source mostly intact.
https://www.microfocus.com/en-us/products/visual-cobol/overview