Ok here's what I turned up in NoveList:
I can't believe I didn't think of this before, but J.D. Robb writes a very popular romantic suspense series where the female detective, Eve Dallas, has to solve a crime, and there is an ongoing relationship with her business partner/boss/lover Roarke. It's set in the not-so-distant future. The first one is called Naked in Death.
Cold Target by Patricia Potter: "Vowing to find the sister she never knew she had, lawyer Meredith Rawson join forces with Detective Gage Gaynor when her search turns dangerous, while her sister Holly, on the run from her controlling husband, desperately seeks a safe haven for her and her young son."
Bodyguard by Suzanne Brockmann: "FBI agent Harry O'Dell's personal vendetta against the mob introduces him to the knockout blond wife of a mafia boss, and his feelings for her present the greatest danger of all."
Glass Houses by Stella Cameron: "NYPD homicide detective Aiden Flynn is drawn into a deadly game of cat and mouse when he receives a cryptic e-mail that leads him to a beguiling British woman, Olivia Fitz-Durham, on a high-stakes and dangerous quest."
Try searching under "romantic suspense novels" and you may find more. I gave you the ones rated most popular in NoveList.