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Also, Karen White's The House on Tradd Street series is about a real estate agent who can see ghosts, it's also a romance.

Here's a list of similar book series, some of which have been mentioned:
Iris Johanen Eve Duncan series; Daynda Jones Charley Davidson series' Karen White The House on Tradd Street series; Charlaine Harris Harper Connelly series; Karen Robards Dr Charlotte Stone series; Kay Hooper The Bishop/Special Crime Unit series

Also: Shiloh Walker - FBI Psychics series