Did you rename the backups? The filename should contain the serial – in recent versions at least.
If anybody knows a better way, please tell. This is
NOT an elegant way, but it works:
With GodMode9:
The serial is stored inside the file
[1:SYSNAND CTRNAND]:/rw/sys/SecureInfo_A
If you open it in the hex-editor you get a lot of binary gibberish and on the very end of the (short) file is the serial.
GodMode9 is able to mount nand.bin images – but only from the same console. If you try to mount an image and you can browse it like
[SYSNAND CTRNAND], it fits for the console.
With a computer:
Set up your computer according to
this tutorial and mount the NAND-image(s) with fuse-3ds and OSFMount (on Windows, Linux should be able to mount the image files with "
-o bind" as mount option). Then navigate to
/rw/sys/SecureInfo_A and open the file in a text editor.