Ok, I have looked for a simple solution on the internet and it seems many people have come up with different not-so-simple ideas. Here's what I came up with on my quiet (and boring) workday on a Saturday:
$ pv original_file > copied_file
2.57GB 0:01:13 [35.9MB/s] [===============================================================================================================>] 100%
In the command above pv is reading the original_file and passing it to stdout. cat is grabbing the output from pv on its stdin (-) and redirecting it to the copied_file. Same apparent effect as copying the file using the cp command.
The pv utility should be available for almost all distros.