set her cap

dated To try to attract, secure, or win someone as a romantic partner or spouse. Said especially (though not exclusively) of a woman in pursuit of a bachelor. Well, if he insists on remaining so inhospitable, then I shall simply set my cap at a man with a greater sense of charm and decency. The ladies of this town shall all be setting their caps at Mr. Rutherford, now that his inheritance has left him quite wealthy. But don't you find it rather unseemly for a man of his age and station to set his cap at a girl who's barely of voting age?

A woman's determination to attract a particular man. In the days when women's attire included head coverings, a woman who wanted to appeal to a man would wear her best bonnet. The phase was wellknown in the 18th century, when Jane Austen used it in Sense and Sensibility: “I abhor every commonplace phrase by which wit is intended; and ‘setting one's cap at a man,' or ‘making a conquest,' are the most odious of all.”