The best story is by Timothy Zahn (who I like an awful lot anyway), and even has Harrington as a character, but it's a tale from back when she was still a cruiser captain hunting pirates in the Silesian Confederacy, and she isn't the main character. In fact, Zahn goes rocketing away from canon by actually having her make a tactical error at one point. It does point out something that the Star Trek writers figured out a long time ago. Ship's captains are a lot more interesting than admirals, so do whatever you have to to avoid promoting your captain out of the command chair.
The other good thing about collections like this is that you'll occasionally discover an author you haven't read before, and turn out to enjoy. This time around it's John Ringo, who has two stories in the book. The man has a sense of humor, and I liked what I read, so I'll probably take a look at some of his novels.
As I was writing this, it occurred to me that I don't feel this way about the other series of books set in a single author's universe that I follow, Larry Niven's Kzin Wars series. Love Known Space, love Niven's stuff (for the most part), don't like most of the derivative works. Huh.