I'm confused by that, Janis. I don't understand why raising the mirror had anything to do with blown highlights.
According to my camera manual, my camera also doesn't meter while the mirror is up. However, if I meter the scene before lifting the mirror, then raise the mirror and then release the shutter, the image is exposed at the values that were metered before raising the mirror.
That's true when I use Aperture priority. If I were concerned about it not working effectively for whatever reason (I'm not concerned), I could use manual metering to lock in the exposure.
I would not know until capturing the image whether there were any clipped highlights but that is true whether or not shooting with the mirror up.
I actually wonder if the camera manuals are written improperly. I imagine that the camera actually does meter while the mirror is up and it's only that the camera doesn't display the metering results in that situation. Indeed, if the camera does not meter while the mirror is up, I would expect all of the camera manuals to recommend using manual metering before raising the mirror and none of the manuals I have reviewed make that recommendation.
By the way, the same camera manuals explain that the camera will not auto focus while the mirror is raised. Yet I can use auto focus while using mirror-up mode and the camera focuses properly. Again, I believe that's because the camera actually is focusing while the mirror is up even though it is not displaying whether focus has been achieved.