Q. If a woman wants to wear tefillin, is there any reason to object?
Thank you.

A. The Talmud (Eiruvin 96a) mentions that Michal the daughter of King Shaul donned tefilin and the sages did not protest. Mishna Berura (301: 158) quotes Magen Avrohom’s (ibid. : 154) ruling that if a woman finds a pair of tefilin on Shabbos is prohibited to wear them in order to bring them in as a clothing article since she doesn’t normally don them. However, Mishna Berura adds, that there are Poskim that permit since in principle by Talmudic law women are not prohibited to wear tefillin.
Rema in Shulchan Aruch (O.H. 38: 3) rules that we do object and disapprove of women wearing tefillin. Mishna Berura (13) quotes the reason of guf naki (body cleanliness) essential for putting on tefillin.
Horav Shlomo Miller Shlit”a pointed out to the words of Piskei Teshuvos in both locations mentioned above. He quotes a number of Poskim that although in principle would allow women to wear tefillin, since today there are not donned constantly. However, he then vehemently and emphatically quoting contemporary Poskim, rules that nowadays it is totally prohibited, even for a woman perusha (separated from the worldly) and extremely righteous. The reason he explains is that it has become a major issue of Reform Judaism. Besides, he points out to the Targum Yonassan Ben Uziel on the prohibition (Devorim 22: 5) “A man’s attire shall not be on a woman.” The Targum translates the above as applying to tefillin and tzitzis.
He also cites Kaf Hachaim (38: 8) on the Cabalistic severe restrictions and extreme care asserted by the Arizal on women wearing Tefillin.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a