From what I’ve seen in various shuls, there is no issue about a woman saying Kaddish if there is a man saying as well. The question seems to be if there is no man saying Kaddish. It seems to me, and I’ve never looked into this at all, the issue is that Kaddish is a “davar sh’bikdusah” and we do not say devarim sh’bikdusha without a minyan. Since a woman is not mitztareif to a minyan, how can she say Kaddish? The flip side to this is if there is a minyan (i.e. 10 men) present, why can’t a woman say kaddish just the same way she might answer to the kaddish of another, or say kedusha in the chazarat hashatz? Does the recitation of a davar sh’bikdusah require that it be said from within a minyan, or merely in the presence of a minyan? I believe the answer is the former, that Kaddish must be recited by someone from within the minyan. By way of analogy, we’ve all seen men, who arriving late for Ma’ariv, say Barchu at the end and everyone answers. That is allowed since the man saying the Borchu is of the minyan. A women, who ran late for maariv could not do that. Again I haven’t looked into this, and these are my knee jerk reactions. I also must add that I have seen women say Kaddish alone in many MO shuls. There is no question in my mind that the rabbis who sanction this practice have a Halachik basis for it.
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