I did DND ~ EDI at some point in the summer of 1998. It was a company called Business Air, as I recall, who had just been bought by BD. It was a Saab 340 and an 11 minute hop. The flight had come from ABZ (again, if memory serves) and was continuing down to MAN. The flight was VERY expensive about £50 for the single but was the only way to get quickly between the two places when needed.
A grand little airport and still there when I looked out of the train window last Friday on my way from EDI to ABZ by GNER.