Not only is it halal, but also desirable, for all Muslims, whether men or women, and how fortunate is the one whose eyes shed tears in the remembrance /fear of Allah:
And they fall upon their faces weeping, and the Qur'an increases them in humble submission. (17:109)
Those were the ones upon whom Allah bestowed favor from among the prophets of the descendants of Adam and of those We carried [in the ship] with Noah, and of the descendants of Abraham and Israel, and of those whom We guided and chose. When the verses of the Most Merciful were recited to them, they fell in prostration and weeping. (19:58)
It was narrated that Abu Hurayrah :ra: said: The Messenger of Allaah :saws: said: “There are seven whom Allaah will shade with His shade on the day when there will be no shade but His: a just ruler; a young man who grows up worshipping Allaah; a man whose heart is attached to the mosque; two men who love one another for the sake of Allaah, meeting and parting on that basis; a man who is called (to commit sin) by a woman of high status and great beauty and he says, ‘I fear Allaah’; a man who gives in charity so secretly that his left hand does not know what his right hand is doing; and a man who remembers Allaah when he is alone and his eyes flow with tears
.” Narrated by al-Bukhaari, 660; Muslim, 1031.
Here is a nice link to read more: