The Daystrom Award was a scientific medal named in honor of Richard Daystrom.
According to a personnel file observed by Deanna Troi in 2370, Anaanda Ziff received the Daystrom Award in quantum physics on stardate 46512.6. She earned the award while serving aboard the USS Enterprise-D. (TNG: "Eye of the Beholder" production artwork)
Harry Kim once joked to Reginald Barclay to make sure to thank him and Seven of Nine when he accepted the Daystrom Award for creating the first Trans-Galactic Com-link between Earth and the USS Voyager. (VOY: "Author, Author")