Take this with a grain of salt as I do not have VSTO, but based on my understanding it is an extended wrapper around the standard office interop.
After copying a worksheet, the newly created worksheet becomes the activeworksheet; therefore you should be able to use that to create a reference.
For standard interop the syntax would be:
Dim newcopy As Excel.Worksheet = DirectCast(app.ActiveSheet, Excel.Worksheet)
where "app" is a reference to the Excel application.
I believe the VSTO syntax would be:
Dim newcopy As Excel.Worksheet = DirectCast(Me.Application.ActiveSheet, Excel.Worksheet)