Although generally one does not answer "Amen" to his own Beracha, our custom is to say "Amen" at the end of a Beracha which concludes a series of Berachot. A very common example is the daily recitation of Yishtabah, which we conclude by reciting, "Melech Kel Hai Ha’olamim Amen." Yishtabah concludes the section which began with the Beracha of Baruch She’amar, and we therefore end with "Amen" as this concludes a series of Berachot. Another example is the series of Berachot recited after the Haftara reading on Shabbat and Yom Tob. The final Beracha of the series ends with, "Baruch Ata Hashem Mekadesh Ha’Shabbat," and the one reciting the Berachot adds "Amen," as this concludes a series of Berachot.
Rav Shlomo Luria (1510-1573) raised the question of why "Amen" is not said at the conclusion of the Beracha recited after an Aliya to the Torah. When a person goes to the Torah for an Aliya, he recites before the reading the Beracha of "Asher Bahar Banu Mi’kol Ha’amim," and then after the reading he recites the concluding Beracha of "Asher Natan Lanu Torato Torat Emet." Seemingly, this second Beracha concludes a brief series of two Berachot, and one should thus say "Amen" at the end of this Beracha. Rav Shlomo Luria answers this question based on a rule established by the Bah (Rav Yoel Sirkis, 1561-1640), which is mentioned also by the Kaf Ha’haim (215), that "Amen" is not recited at the end of a series of Berachot which relate to the same subject. Both Berachot recited over the Torah – before and after the reading – praise G-d for giving us the Torah, and thus "Amen" is not recited at the conclusion of the final Beracha.
The Bet Yosef (commentary to the Tur by Maran Rav Yosef Karo), in Siman 215, cites from Rav Levi Ben Habib (1480-1541) that one should not add "Amen" upon concluding the Beracha of "Boreh Nefashot." This Beracha concludes, "Baruch Hai Ha’olamim," which resembles the conclusion of Yishtabah ("Melech Kel Hai Ha’olamim"). However, whereas "Amen" is added at the end of Yishtabah, because, as mentioned earlier, it concludes a series of Berachot, one does not add "Amen" at the end of "Boreh Nefashot." It should be noted that Rav Shalom Mesas (1909-2003) records a custom among some to add "Amen" at the end of "Boreh Nefashot," but our practice does not follow this view, and we do not say "Amen" after "Boreh Nefashot."
Incidentally, our custom is to conclude "Boreh Nefashot" with the words "Baruch Hai Ha’olamim," as opposed to the custom among Ashkenazim to recite "Baruch Heh Ha’olamim."
Summary: One adds "Amen" at the end of a Beracha which concludes a series of Berachot, and thus "Amen" is recited at the end of Yishtabah and at the end of the final Beracha recited after the Haftara reading. Our custom is not to recite "Amen" at the end of "Boreh Nefashot," even though the Beracha’s conclusion ("Baruch Hai Ha’olamim") resembles the conclusion of Yishtabah ("Melech Kel Hai Ha’olamim").
