Cannot restore iTunes backup - not enough space! I am trying to restore an iTunes backup of my daughter's iPhone SE that was made via iTunes on a Mac. 

The Mac runs macOS 10.14.1 and iPhone is running iOS 12.1

When I click "Restore Backup" it starts a progress bar, counts down for about five minutes and then says "Not enough space on iPhone".

This seems bizarre to me - surely the backup is some sort of snapshot of the contents of the exact same phone, so how can it now be too large to fit back into the phone?

Apple Support simply suggest Restore iPhone (i.e. erase everything) and hope that the backup works then - obviously since the backup has already failed, I am reluctant to double down on it.

Is there any way to find out how much extra space is actually needed?
You could back the device up to iCloud or another Mac if you suspect the current backup isn’t good. If you’re willing to forego that extra safety, net then the first thing is to erase all content and settings to see how much space is free. 

Try the restore again and then optionally restore the device.  I’ve seen this happen on rare occasion - especially on iOS devices with the smaller flags storage if they’ve been updated over the air a few times. It also could be a sign the storage on the device has started to fail. When SSD fail, they just mark blocks as bad and you get less free space than normal. 

You could also make an iCloud backup, omitting some of the apps you don’t need to back up so that the payload is less size. Tap through the settings app and iCloud and manage storage and the device in question. Then turn off the largest items you don’t need (not shown below the content is the apps in CHOOSE DATA TO BACKUP)



Just turn off some and make a second backup in case you need a smaller iCloud backup to restore as a last resort.