I just did this, on hekate ( I'm on the latest) I went into the tools tab, clicked on where it says Backup eMMC and it gives you 4 options to choose from(boot 0&1, eMMC RAW GPP, eMMC sys, eMMC user), at the bottom of this screen there should be something that says 'SD emuMMC Raw Partition' you'll want to click on it and it'll say on and then the options to do back up will be SD emuMMC boot 0 & 1 and SD emuMMC RAW GPP go ahead and do both. The backup of your boot 0&1 files and full emuMMC backup will be in the in the folder backup/(random letters)/emummc. You need to put the files into restore folder within the backup folder. you'll want to transfer those files in the backup folder to the new SD along with the folder emuMMC folder in the root of the SD card to the new SD card. Before you transfer the files you'll want to heave already created a partition for the emuMMC in the new SD card along with your other files for hekate and atmosphere and whatever else you'll be transferring onto the SD card. Remember that when you create the new partition on the new SD to only have the essential files to load into hekate or if you have too many things it wont be able to backup your files already there and you'll need to retransfer them. Once your SD has the new partition and is ready to restore you'll go back into the tools tab in hekate and this time hit restore eMMC, once again you'll click at the bottom where it says SD emuMMC Raw Partition so that it restores to the partition and not your regular emmc (it'll show on after you touch it) restore your boot 0 & 1 and your raw gpp. Your new SD should now have your emuMMC from your original sd.
One tip is when you transfer your emuMMC folder from the root of the original SD card don't transfer over the emummc.ini with in because the new SD card will create a new one when you create the partition on your new SD showing which sector to look for the emuMMC, if you do overwrite it the simple fix within hekate is to go to emuMMC on the home tab, hit migrate emuMMC and click Fix Raw, it'll rewrite the correct sector on the .ini file. I hope this helps, this is what I went through to transfer my emuMMC onto a new SD card. It is really simple from what I went through and I'm sure if you haven't done it yet what I wrote will help you out and sorry for long sloppy paragraph as it's late where I'm at.
To also answer one of your previous questions you'll basicallly need 30 free gigs on your original SD card to make a backup to fit everything at once.