I've installed Mint 16 x64 on UEFI a few times now, both to an internal SSD and to a USB 3.0 stick. I have a brand-new system that consists of an Intel DH87RL motherboard. I am beginning to suspect that there are some bugs in the x64 installer that do not deal properly with UEFI machines. The installer reports that it finished, but upon reboot, the system fails to boot.
If you are having problems, go down this list and make sure you have everything.
1. You MUST have a GPT formatted disk.
2. You disk MUST have an EFI System Partition, and it MUST be formatted FAT32
3. The UUID of your EFI System Partition MUST be "70D6-1701" (I don't know why this is, can someone else explain it?). This seems to be a bug in the various Linux utilities that they will set the UUID of the EFI System Partition to SomethingElse, and I have yet to find a Linux utility that will allow me to change the UUID of a disk (again, help would be appreciated with this).
4. The /etc/fstab of your installed system MUST refer to your EFI System Partition with the UUID "70D6-1701", and mount it at /boot/efi
I have found that the easiest way to accomplish this is to format my disk under Mac OS X, since I happen to have a MacBook available. I have tried using Linux disk utilities to do this, but something always goes wrong. Apple has been using EFI sine the earliest Power Macintosh systems hit the market in the 90's, and obviously has used EFI since Day One of switching to Intel, so I figure Apple probably has a bit more expertise with EFI thatn everyone else.
After formatting my disk on the Mac, then running the live USB installer, selecting "Something Else", and specifying the EFI System Partition, my root partition (I don't do swap partitions), and telling it to put the bootloader on the EFI System Partition (which after much research seems to be the correct way to do it), I have found that the Mint Installer doesn't always copy the bootloader files to the EFI System Partition.
Fortunately, my DH87RL motherboard has a built-in UEFI shell, so I can drop to the shell and diagnose this problem. Int eh UEFI shell, you should see fs0: as your EFI System Partition. On this drive should be a folder called "EFI". In there, there should be a folder named "BOOT", and a folder called "ubuntu". I say, "should", because in the several times I have done this install, only ONE TIME has the Mint Installer actually copied these files to the correct location on the correct disk. (Yes, the new system also has an HDD with Windows 7 x64 on it. This machine is going to my mom and the niblings for Xmas.). If you have previously installed Windows x64 on this disk, you may also see "EFI\Microsoft".
In "EFI\ubuntu", there should be a bunch of files: "shimx64.efi", "bootx64.efi", "MokManager.efi", and "grub.cfg". The "grub.cfg" file MUST have the UUID of your root partition in it.
IF your installer didn't function correctly, you will find these files under "/boot/efi" on your newly installed root partition. You will need to copy them to the EFI System Partition. IF you installed from the Live USB, you should have a bootable system to do this.
Once you have all of this the way it's supposed to be, you *should* have a working system. Now you can boot it up, and fiddle with GRUB2 to get it to recognise your Windows installation, too.
[IF your motherboard's BIOS is wonky, like mine is with the Intel DH87RL v322, you may need to copy "bootx64.efi" to "fs0:\EFI\BOOT\BOOTX64.EFI". You're not *supposed* to have to do this according to the UEFI standard, but the DH87RL BIOS is buggy, and the only way it will recognise an HDD as bootable is if it sees that file. Also, on the DH87RL, you have to leave legacy boot enabled, or it doesn't work, and your PCIe video card will also not work, and you will tear you hair out for hours trying to figure out why...but that's another story.]