I have a Slackware 14.2 UEFI mode install and I need to move the disks from a PC that died into a replacement PC (same make and model PC). I also compile my own kernels, so I don't want to remove/overwrite any of those in the EFI directory if possible.

Can I boot into a Slackware 14.2 install CD (or Eric's Slackware Live Edition) and do the following to make the boot entry in NVRAM? /dev/sda1 is the EFI partition and this is an mSATA drive.

I've seen mention of using eliloconfig but I don't know if it's designed for this type of situation.

I don't have much experience with UEFI, other than the 14.2 install about a year ago, and I've heard bad things can happen if this isn't handled correctly so I just want to be safe.

Probably your machine will boot as the previous one without doing anything, as you already have all that's needed in the ESP (EFI System Partition), provided there be no change in the partitions' naming.

If you also want to have a boot entry for Slackware in your new machine firmware's menu (in NVRAM) you can either type the efibootmgr command manually as root, or run eliloconfig, which will kindly proposes you to do that for you, as you like.

Thanks Didier. I should have mentioned that I've installed the boot disk but the new PC just boots to an EFI command line prompt (EFI Shell Version 2.31). The BIOS does recognize the disk and has it listed third in the boot order, but it won't boot from it. The disk is also appears to be listed as fs0 in the EFI Shell, but it won't boot from the EFI menu either. I'll try eliloconfig, as it has some safety checking in the script.

Well, using the EFI shell you should be able to load the file elilo.efi. Use the built-in helps to find the commands, or a web search engine with "EFI shell commands" as argument.

I ran the efibootmgr command I listed above (from the Slackware 14.2 install DVD) and the PC now boots into Slackware automatically. I did see some warning/error messages flash by on the console, but I'll try to catch them and then research.

For the records and per the UEFI specification, the firmware should load automatically the boot image, provided it be (re)named BOOTx64.EFI.

As you have an EFI shell, another solution would be to write a small text file /boot/efi/startup.nsh with only this line:
EFI\Slackware\elilo

To know more see the UEFI Specification Version 2.7 and the UEFI Shell Specification Version 2.2 (the latest at time of writing) can be downloaded from this page.