I just wrote a terrifyingly long post about my struggles putting games on my NAND for melonDS
here. But it talks about backing up saves! : ) I don't know if it's different from 3DS, but for DSi, you dump your NAND, call it "NAND.bin", then decrypt it using the tools at the top of the thread I've linked to. Then you use OSFMount to mount your NAND as a removable drive, open up the "title" folder, open up the "00030004" folder, then look for your game's ID, which you can probably find
here. Then, in the folder, there should be a "data" folder-- with a .sav file in there that contains your save information. : ) You would then put that save in the same directory in the decrypted NAND you'll format for melonDS, once again, using the tools in the thread linked. Hope that helps-- once again, it might be a slightly different procedure!
EDIT: If you jailbreak your 3DS, you can install
Checkpoint to save out most savefiles-- for GBA VC files, you follow instructions
here.