For anybody who wants to try this themselves, or wants to sharpen drill bits generally, getting the concentricity of the point and the shank accurate is absolutely key.
For normal-sized drills, at best you're going to drill an oversized (and likely tapered) hole. When you get into the smaller sizes, you're going to break bits left and right.
For normal-sized drills an everyday drill sharpening gauge should do the trick. That'll stop being useful long before you get down to 0.5mm.
If you're drilling wood or some other soft material, and you've got bar stock of the right diameter around that isn't hardened (i.e. a nail), you can sometimes get away with clipping the end of the nail off with a pair of diagonal cutters and peck drilling. You have to peck because the shank fills the hole so there's no way to clear the chips.