Are Women Obligated in Zimun?

When three or more people share a bread-based meal, there is an obligation to preface Birkat Hamazon with Zimun, that is, a summons to join the blessing. This obligation is deduced from the verse (Devarim 32:3) “Ki Shem Hashem Ekra Havu Godel Lelokenu” (lit. “When I call Hashem’s Name, attribute greatness to our G-d”). The Shulhan Aruch (Orah Haim 199:7) writes that although women are not obligated in Zimun if they eat among themselves, they are nevertheless permitted to recite. The Vilna Gaon writes that women are actually obligated to say Zimun if they eat among themselves and indeed there are communities, especially in Jerusalem, where this is practiced. The Shulhan Aruch adds that when women eat with men, they are obligated to listen and respond to the Zimun. It should be noted that men and women do not recite Zimun together as it is considered a sign of immodesty, and thus women are not counted towards the minimum of three needed for Zimun.
There is a misconception that women are exempt from Zimun when men and women eat together and that they may recite Birkat Hamazon individually. Nevertheless, Rabbi Moshe Feinstein (Igrot Moshe, vol. V, Orah Haim, § 9:10) writes that in a situation where, for example, a woman is constantly between the kitchen and the table while serving the meal and does not have the chance of being part of the meal, she would be exempt from listening and responding to Zimun, and could recite it on her own. If, however, a woman is part of the meal, this leniency does not apply and she would be obligated in Zimun.
Summary:    Women who eat among themselves are exempt from Zimun, but may recite it. Women who eat among men are obligated to listen and respond to Zimun. A woman who does not have a chance to be part of the meal due to serving, etc, may be exempt from Zimun.