I have several recurve blades of varying degrees. I sharpen all of them with my chef's diamond rods. You can Google DMT diamond sharpening rods, or just "diamond sharpening rods" and come up with other makers as well. I bought a medium and an extra fine, and they take care of all my needs.
I use a Kershaw Tremor a lot at work and it has a fairly pronounced recurve. A few licks on the rods and it is back to snuff easily. Same with my Kershaw Tyrade, and the opposite of a recurve, the Junkyard Dog II. It's large belly makes it hard to sharpen on stones, but easy on the long chef's rods. A few (or several!) swipes on the rods do the trick, and for a tune up I just use the extra fine.
I have been sharpening my kitchen knives and all my recurves on rods for years. As far as reliability and durability go, before my last set of rods wore out after about 10 years after literally thousands of sharpenings of kitchen knives, camp knives, and of course my recurves.
If you have any experience with freehand sharpening at all, the rods make a recurve a snap to sharpen. Even if you don't, rods are so easy and intuitive to use it makes sharpening different shapes a breeze.
Robert