Below are a list of recommendations, all of which fall into the speculative fiction category and all of which are set during the Georgian/Regency eras.
Pride and Prejudice, like the majority of Austen's work, is classed as a Comedy of Manners. Tooth and Claw, on the other hand, is a Fantasy of Manners; it's very much a parody of the regency style stories, with one particular twist - the entire cast of characters are dragons! After the death of the family's patriarch, five siblings - two brothers and three sisters - fight for their inheritence, fall in love and become involved with the abolition movement. This is a family trying to find their way in the world, even if they have to fight tooth and claw...
This may seem like a peculiar recommendation as there aren't all that many similarities between these two stories, but they're not entirely dissimiliar either. What links these two are heroines who yearn for adventure, particularly adventure of the supernatural kind! While young Catherine Morland loses herself in the thrills of Gothic fiction, young thief Lila longs to be a pirate captain and see the world.
These two are perhaps the most similar books on this list. Sense and Sensibility tells the story of sisters Elinor and Marianne, while Shades of Milk and Honey tells the story of sisters Jane and Melody. Both sets of sisters - including an older, serious sister and a younger, more beautiful sister - must compete with the women around them to find suitable matches. The only real difference is Jane and Melody have the benefit of magic.
In contrast, these two are probably the most dissimilar books on this list, but in some ways I see these two as two sides of a similar story. Persuasion tells the story of Anne Elliot, a 27 year old spinster who, nine years before, was persuaded to break off her engagement to Captain Wentworth due to his uncertain circumstances. Wentworth went to fight in the Napoleonic Wars and has returned from war wealthy and very eligible, and Anne must struggle with the feelings she still has for him. Temeraire, on the other hand, tells the story of Will Laurence who must fight in the Napoleonic Wars. With dragons. If you're a fan of Persuasion, perhaps you could read Temeraire and pretend Wentworth is off riding a dragon of his own somewhere.
Emma is one of Austen's most beloved heroines who takes matchmaking into her own hands to become the regency Cupid. Kat, the heroine of Stephanie Burgis's middlegrade series, is equally as hands-on. When she discovers she has inherited her late mother's magical gifts, Kat takes it upon herself to help her older sisters win their true loves and rescue her family from the sinister Sir Neville.
In contrast to what is possibly the most fun of Austen's novels, Mansfield Park is quiet, subtle and more serious. The heroine of Mansfield Park, Fanny Price, is sent to live with her mother's sisters at their lavish estate after her own large family - Fanny is one of nine children - falls into destitution. Only one of her cousins, Edmund, makes any effort to make her welcome, making her feel, for the most part, like an outsider in her own home. The Winter Witch, on the other hand, is set in early 19th century Wales. Morgana, a gypsy's daughter, hasn't spoken since she witnessed the murder of her father, and as such she is something of an outsider in her small Welsh town. Concerned for her safety amongst her superstitious neighbours, Morgana's mother marries her off to Cai Jenkins, a widower from the far hills. Initially heartbroken at being torn from her mother, Morgana slowly falls in love with the wild land surrounding her new husband's farm.