There is a Misva to train children to count each night of the Omer with a Beracha. Each night throughout the Omer period, a parent should recite the Beracha over Sefirat Ha’omer with the children and count with them, to train them in the Misva.
Hacham Ovadia Yosef, in his work Yabia Omer (vol. 2, Siman 13), writes that a parent should have the child count the Omer with a Beracha even if the child had missed a day of counting. When it comes to adults, as we know, somebody who missed a day of counting continues counting the subsequent nights without reciting the Beracha. However, Hacham Ovadia rules that this does not apply to children, and they should recite the Beracha over Sefirat Ha’omer even if they had missed a day. He explains that the prohibition of reciting a Beracha Le’batala (a Beracha in vain), which is derived from the verse, "Lo Tisa Et Shem Hashem Elokecha La’shav," does not apply to children. Children may recite Berachot as part of their training, even in situations where a Beracha would not technically be required, and thus when counting the Omer, too, children should recite the Beracha even if they had missed a day of counting.
Women are exempt from the Misva of Sefirat Ha’omer, as it falls under the category of "Misvot Aseh She’ha’zman Gerama" ("time-bound" Misvot), which generally do not apply to women. Strictly speaking, a woman may count the Omer if she so wishes, despite her exemption, though without a Beracha. According to Sephardic custom, a woman may not recite a Beracha over a Misva from which she is exempt but chooses to fulfill, and therefore a woman who chooses to count the Omer should not recite a Beracha.
However, the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) writes that according to Kabbalistic teaching, women should not count Sefirat Ha’omer at all. The Ben Ish Hai notes (in his work Rav Pe’alim) that this was the view of the Arizal (Rabbi Yishak Luria of Safed, 1534-1572), and this is also the ruling of Rabbi Eliyahu Mani (Baghdad-Israel, 1824-1899). From the Kaf Ha’haim (Rav Yaakob Haim Sofer, Baghdad-Israel, 1870-1939), by contrast, it appears that a woman may count the Omer, though without a Beracha.
Our practice is to advise women not to count Sefirat Ha’omer at all, in accordance with Kabbalistic teaching.
Ashkenazim follow the view that a woman who voluntarily performs a Misva from which she is exempt may recite the Beracha. Interestingly enough, however, the Mishna Berura (Rabbi Yisrael Meir Kagan of Radin, 1839-1933), in Siman 489 (3), cites the Shulhan Gabo’ah as ruling that even according to this custom, women should not recite the Beracha over Sefirat Ha’omer if they decide to count. The reason, as the Mishna Berura cites from the Shulhan Gabo’ah, is that "they will certainly forget" one of the days of the Omer. It is unclear from the Mishna Berura’s citation what precisely the Shulhan Gabo’ah had in mind, but when we look at the original text of the Shulhan Gabo’ah, we immediately understand his intent. It is very common for people to forget to count a day of the Omer, and in such a situation, as mentioned earlier, the Beracha over the counting must be omitted on subsequent nights. The Shulhan Gabo’ah feared that due to women’s limited knowledge of Halachic minutiae, a woman who counts the Omer and forgets a day will not know that she must now count without a Beracha. She will thus end up reciting many Berachot Le’batala. Therefore, he ruled that it is preferable for a woman who decides to count the Omer to always count without a Beracha, in order to avoid complications.
Clearly, however, this concern would not apply nowadays, when women attend schools from a young age and receive a comprehensive Halachic education. Unlike in the times of the Shulhan Gabo’ah, women today certainly have the Halachic sophistication to realize that they must count without a Beracha if they missed a day of counting, and therefore, as long as they did not miss a day, they may – according to Ashkenazic custom – count the Omer with a Beracha.
As mentioned, however, Sephardic custom forbids women from reciting a Beracha over Sefirat Ha’omer, and our practice is to advise women not to count altogether.
Summary: Children should be trained to count Sefirat Ha’omer each night with a Beracha. A child who missed a day of counting should nevertheless continue counting each night with a Beracha. Women are exempt from Sefirat Ha’omer. From a strictly Halachic standpoint, a woman may count Sefirat Ha’omer, though without a Beracha (and according to Ashkenazic practice she may even recite a Beracha). For reasons related to Kabbala, however, our custom is to advise women not to count altogether.
