Women are exempt from the mitzva of counting the omer, for it is a positive time-bound mitzva. If a woman wishes to fulfill this mitzva, it is a credit to her. As we have learned (above 2:8), according to Sephardic custom she does not recite the berakha, but according to Ashkenazic custom she may recite it.
However, even within Ashkenazic custom, some poskim are worried that since women are not present in the synagogue at the time of the counting of the omer, there is a reasonable concern that she will forget to count one day without realizing it and then continue counting with a berakha. According to halakha, one who forgets to count one day may not continue counting with a berakha, and if she does, according to some, it is considered a berakha le-vatala. To avoid this problematic situation, some say that even according to Ashkenazic custom it is best that women do not recite a berakha on this mitzva (MB 489:5). Others say that women should not count the omer for kabbalistic reasons (Rav Pe’alim, vol 1, Sod Yesharim 12). In contrast, some say that Ashkenazic custom is that women count the omer (MA 489:1). Therefore, according to Ashkenazic custom, whoever knows that she will be able to complete the entire count and that she may not recite a berakha anymore if she forgets, may recite a berakha. In particular, this pertains to women who regularly pray Ma’ariv or who are reminded to count the omer daily at home, as there is minimal concern that she will forget to count the omer. If there is a reasonable concern that she will forget to count one day, it is preferable that she not count with a berakha.