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Lois McMaster Bujold: The Spirit Ring

In an alternate Renaissance Italy where the church regulates magic and licenses magicians, fiery Fiametta Beneforte wants to be more than her goldsmith-mage father's unpaid apprentice. But when the Duchy of Montefoglia is laid under military and magical siege, she unexpectedly must join with Thur Ochs, a young Swiss miner and foundryman, to tap their skills in both metalwork and necromancy to rescue her father's soul and combat an evil sorcerer.

Elizabeth Moon: Once a Hero

Esmay Suiza left her home planet of Altiplano to join the Regular Space Service, even though her family expected her to become the Landbride of their estancia. Altiplano is only an affiliate world of the Familias Regnant; they have no Seat in Council, and Esmay is not a command track officer...until, as the senior survivor of a mutiny, she takes command and saves the day. Now she's under some suspicion--why had she hidden such ability?--and takes a long leave at home. But old wounds return, and she returns to the Fleet, to be assigned to a Deepspace Repair Ship in her "proper" role as technical track. There she meets Barin Serrano, Heris's relative...and there she learns that ability cannot be hidden easily.

Zen Cho: Sorcerer to the Crown

Zacharias Wythe, England’s first African Sorcerer Royal, is contending with attempts to depose him, rumours that he murdered his predecessor, and an alarming decline in England’s magical stocks. But his troubles are multiplied when he encounters runaway orphan Prunella Gentleman, who has just stumbled upon English magic’s greatest discovery in centuries.

The protagonists in this one may be a bit too competent at the start to fit your criteria -- at least Zacharias, who is an educated sorcerer at the beginning of the book (but still has a lot to learn). It's a really good book, though, and has one of my favourite quotes in any book ever:

Originally Posted by Sorcerer to the Crown

Prunella had once thought life in London would be all flirting and balls and dresses, hitting attentive suitors on the shoulder with a fan, and breakfasting late upon bowls of chocolate. She sighed now for her naïveté. Little had she known life in London was in fact all hexes and murder and thaumaturgical politics, and she would always be rising early for some reason or other!