Files removed during failed copy

I was copying a large folder holding a recording session I'm working on to an external hard drive. I left the room and came back to an error saying that copying failed. After this I realised almost of the files are gone from the computer and hard drive. Is there any way to recover this data?

Not cheaply. There are a couple of products I've used that worked reasonably well. Data Rescue 3 (you can search for it) works really well and may be the best.

I think before you invest in data recovery software, that you need to figure out why the files from your computer are no longer there. Files just don't disappear during a copying session unless there has been some sort of failure with the hard drive.

Copying to where?

If an external hard drive, first check that out.