From what I was taught, there is nothing halachically assur for a woman to say kaddish. While it is not usual for her to do so, neither is she forbidden from doing so in a tzniusdig manner.
Kaddish for an aveil is the verbal affirmation of Hashem’s greatness at a time when people could potentially chalilah have a “tainah” to Him for taking away their loved one. It is just as important for a woman to accept Hashem’s decree, as it is for a man. And if it gives her nechoma to actively show her acceptance and also show kovod to her deceased love one and feel she is helping the iluy of the neshama, who are we to criticize, when it is within the parameters of the halacha?
Personally, I would prefer to have a male whom I know will faithfully attend the minyan every day saying Kaddish on my behalf, but I know a woman who faithfully came to shacharis every 6 AM weekday (and hashkama minyan on Shabbos)for 11 months after her mother died in order to say Kaddish, with the Rov’s haskamah. She was very makpid not to miss the davening (I believe she made mincha and maariv, too, but I cannot swear to it).