I'd like to hear other answers (I'm no expert), but here's my two cents.
First, let's be sure we mean the same thing when we talk about "highlights." You often hear the terms highlights, midtones, and shadows. Highlights are simply the brightest areas of your image. A highlight is said to be blown-out if any one of the three channels (R, G, or B) is at the threshold. To see blown-out highlights, you need to look at the individual channels (R, G, and B) separately, not just the combined RGB values that you see when you check the "Double Threshold" box. Typing capital-H on the keyboard will show these using separate colors on a black background. For example, green pixels indicate that the green channel is blown, while yellow indicates that both red and green channels are blown. Hopefully, you will see an entirely black screen, meaning none of the highlights is blown out. Type capital-H again to toggle back into normal mode.
While making global adjustments in the Develop section of the edit list, you can always use the Protect Highlights slider to prevent highlights from blowing out. If your raw data contains blown-out highlights to begin with, there's no way to recover them. You can only try not to make a bad situation worse.
For example, if you want to sharpen highlight areas that contain some blown-out highlights, you could always sharpen those areas selectively using USM in Darken Only mode. This darkens the darker side of the edges, leaving the lighter side unchanged.