One way is to spread out the too-high value across neighbouring pixels, so-called bloom. This helps in creating a sensation of brightness even if of course no pixel actually has a higher value than 1.0.

The easiest way is to make a copy of the image, subtract 1.0 from the copy, blur that a bit and then add it on top of the original. This should of course be done before you go into gamma space, at which point you do clamp to 1.0.