Hi,
Copying the project should be enough even for regular VS projects (if you want to open both the original and the copied project in one solution, you would need to change the project GUID in the copy). From the VisualGDB side, unless your .vgdbsettings files contain hardcoded absolute paths, simply copying should be enough.
If it doesn’t work, please let us know your project type and the errors you get and we will advise further things to check.