Awe and Trembling
The Komarna Rebbe wrote in his sefer Shulchan Tahor (215 4) that the holy Zohar, and even the Arizal, expounded on the punishment of one who is mevatel the mitzvah of answering amen, and in contrast, described at length the reward of one who is careful about answering it. One who delves into their words “will be gripped by fear and trembling. Therefore, a person should be very careful to answer amen with great kavanah and yishuv hada’as...and he should be careful to answer ninety amens after brachos and Kaddish...”
The Gematria of Amen With the Milui
The Komarna Rebbe further wrote (ibid in Zer Zahav, se’if kattan 2) that the numerical value of his name יצחק יהודה יחיאל is 297, which is the same as the gematria of the word amen in the full spelling [ף“אל ן“נו ם“מ], and in light of this, the Rebbe concludes with a request: “That I should merit to be mekabel Pnei HaShechinah with the light of 370 nehorin,” which one merits in the zechus of answering amen.
The Minhag of the Baal Shem Tov
Regarding teaching children to answer amen, the Rebbe Rav Yitzchak Eizik of Komarna wrote in his sefer Shulchan Hatahor (98 3):
“It is a kosher minhag...that a melamed of children brings the tinnokos shel bais rabban to the shul to answer amen and Yehei Shemei Rabbah and Kedushah in a pleasant voice. This is what Rav Yisrael Baal Shem Tov did in his childhood, as he gathered all the tinnokos shel bais rabban to the shul to answer “Amen yehei Shemei Rabbah.”