It depends on why you need to know what your ketone level is. If you need to maintain a particular level in order to treat some medical problem, then you will probably want to measure throughout the day. But if you are just curious, then there really is no optimal time of day to measure. If you want to track your readings from day to day, however, then take them at the same time of day, under consistent circumstances. For example, you could take a reading at eight o’clock every morning, just before getting out of bed and before eating or drinking anything. Or you could take a reading a eleven o’clock every evening, four hours after your last meal of the day. You get the idea.
But I should probably mention that Dr. Phinney, in a couple of lectures on-line and at Ketofest last year, says that while the serum β-hydroxybutyrate level of 0.5 as the beginning of nutritional ketosis is somewhat arbitrary, he and Professor Volek chose it because that is the level where they generally start to see the benefits of ketosis. They both admit that many of the keto-adapted athletes they have studied were clearly in ketosis but showing much lower levels of β-hydroxybutyrate.
Furthermore, Dr. Phinney has said that, while a reading of 1.0 might be a bit more beneficial than a reading of 0.5, a level above 1.0 doesn’t appear to show any further additional benefit. He even said in one lecture I’ve watched that, while the young people at Virta Health like to compete to see who can get the highest ketone reading, he has to strictly forbid them from passing that attitude on to their patients. So unless we are trying to treat some condition that might be benefited by higher ketone levels (such as Alzheimer’s disease, or certain types of cancer), it really doesn’t pay to worry too much about what our ketone level is.