Austenesque novels typically fall into one of three categories: variations, alternate universe, or sequels. All three have their own set of pit-falls the author must avoid for the story to be worth reading.
In my mind, the sequel is the easiest to sell to the reader, but the hardest to write. Readers want more of their favorite characters; that's why this genre exists in the first place. However, Jane did a wonderful job tying up loose ends, so it's hard to find an actual plot to work with. After all, plot requires conflict, and the pictures of perfect domestic felicity we find at the end of her novels might seem, at first look, to negate the possibility of the lovers ever suffering discord.
To get past that, the sequel author needs to remember that Jane Austen painted a realistic picture of people and life. People are not perfect, even when their love story has the perfect ending. For instance, I imagine that Emma continued to meddle and Knightley did not stop chastising her for it. Both were improved by the events of the book, but neither were perfected. It is the task of the Austenesque author to find which foibles of personality would carry on into marriage, and how that might affect the couple's future happiness.
In Mr. Darcy's Secret, Jane Odiwe excels at this. Her Darcy and Elizabeth are every bit as much in love with each other as we imagine them to be from Pride and Prejudice's conclusion. However, like all newlyweds, there are things they don't know about each other. Elizabeth in particular is troubled by letters she's found that indicate Darcy might once have loved another lady.
At the same time, his decision that Georgiana must make a good match disturbs Elizabeth. She knows her sister-in-law has formed a tendre for a landscape artist, and the marriage Darcy has in mind for her will not make her happy. Darcy's insistence on an alliance of equal fortune and importance seems hypocritical to her, given that he gave up both to marry her.
Both of these plots are very true to the characters. The story progresses in a manner that allows us to learn more of all our favorite characters from Pride and Prejudice, as well as getting to know Georgiana better yet. By the end, of course, all the misunderstandings are resolved. Life at Pemberley is happy once more.
And that is the true art of an Austen sequel: It takes our characters from the happily ever after we see at the end of the book, through another conflict, and brings them back to a happiness made more complete by a greater understanding of one another. If you wish to see this in practice, I highly recommend Mr. Darcy's Secret by Jane Odiwe.