If a device specifies that it can support sd cards up to 64gb, would larger sizes work as well?

I had a look around and found this page here, and here.

In summary, there are three classes of SD cards:

• SD, upto 2GB in size, formatted in FAT12 or FAT16
• SDHC, from 2GB - 32GB in size, formatted in FAT32
• SDXC, from 32GB - 2TB in size, formatted in exFAT

Regular SD cards, and microSD cards are capable of any of these classes. SD card class support is backwards compatible (e.g. SDHC cards are supported in a device that supports SDXC cards), but not the other way round (e.g. SDXC cards are not supported in a device that only supports SDHC).

Because a device that supports a 64GB card must already support SDXC cards formatted in exFAT, I don't see why a larger card wouldn't be supported either. But, a card that supports upto 32GB of size only supports SDHC cards, and therefore not capable of using the larger SDXC cards.

Please remember though that there may still be devices that will not support over 64GB SD cards (even though they theoretically should), possibly due to hardware or software limitations.

I've upgraded the OS of my Galaxy Note 3 to Lilipop and now I'm using a 256GB card and it still work fine.

I have a Samsung Galaxy Note 3, the manual said it has a 64GB limit on SD card but I'm using it with a 128GB card and it works.