Process Explorer: How to check what process is holding my external disk?
Hit menu Find -> Handle or DLL... and then put in the drive letter for your external drive, for example, F:\. This should show you a list of all of the processes holding handles (links to files) on that drive.
From @nwboson: Be sure to run procexp.exe as an administrator to ensure you are searching all processes. That is, don't just click on Process Explorer to run it, but instead right click it and do a 'Run as Administrator'.