Beracha on Voluntary Mitzva Performance ברכה על מצוות רשות

Chiddushei Ha-Ritva, Pesachim 7b

And the reason that our sages said to recite a beracha before performing a mitzva is in order to sanctify oneself first with the beracha and reveal and make known that one performs it [the mitzva] because of the command of God, may He be blessed. And further, because the berachot are a service of the soul and it is fitting to put the soul’s service before a [mitzva] act, which is service [by means] of the body.

Or Zarua II Rosh Ha-shana 266

Rav Yitzchak bar Asher, of blessed memory, was in doubt – in the context of Rabbi Yose and Rabbi Shimon’s position – as to whether [women] can make a beracha over shofar or over other mitzvot in which they are not obligated, if it is considered a [proper] beracha or not.
Since we permit them to blow even though it is a rabbinic prohibition [for it is a form of muktzeh to blow shofar outside of the mitzva on Rosh Ha-shana], that implies that they are doing a good thing and they receive a reward. So they also make a beracha, for it is an optional [mitzva] for them to fulfill like men.
Or perhaps we permit them [to blow] because, since the rabbinic prohibition and blowing on Rosh Hashana is permitted to men – for a man who wishes to blow shofar all day long may do so, even though he already fulfilled his obligation – there is likewise no rabbinic prohibition for women. But how can she recite the beracha ‘Who has sanctified us and commanded us (vetzivanu)’ when she is not commanded?

Hagahot Maymoniyot, Laws of Tzitzit, 3:40

It is a great astonishment, for how can she say “Who has sanctified us in His commandments and commanded us” in a matter that they [women] are not commanded in, not on a Torah-level and not rabbinically?…How can they say “vetzivanu?”

Or Zarua II Rosh Hashana 266

And [Riva] wrote in the name of Rashi that he would prohibit [women from reciting a beracha on voluntary mitzva performance].

Ran on the Rif, Rosh Ha-shana 9b

One who is not commanded and does also receives a reward. Therefore they [the women] are within the mitzva. For they recite a beracha, and we do not say: Since they were not commanded, how can they say “ve-tzivanu” [and He commanded us]? … For it is not difficult, because since the men were commanded and [the women] also receive a reward, they can well say “ve-tzivanu.”

Responsa Yosef Ometz 82

Since I saw the Heavenly response to Rabbeinu Yaakov of Marvège, as I wrote in Birkei Yosef, I have been accustomed to tell women to make aberacha on the lulav as was the old custom that women have practiced in the holy city. Although our master [Shulchan Aruch] ruled that they should not make a beracha, it seems that if he were to lay his holy eyes on Rabbeinu Yaakov of Marvège’s responsum…certainly he would rule and implement custom like this. And in this case the principle “it is not in Heaven” is irrelevant, since there are many great halachic decisors who maintained that [women] may make berachot, it enables us to rule in accordance with them as we have Heavenly support.

Responsa Yabia Omer Part 5: Orach Chayim 43

For we did not come to rule for Ashkenazi women to do the opposite of the Rema’s ruling… Rather we have come to rule for Sefardi women (who according to the testimony of the elders of the sages of the generation of the Chida practiced thus [making berachot] without knowing [any better]) to return to the ruling of the Rambam and our master [the Shulchan Aruch], that they should not recite a beracha in vain.

Mekor Chayim for Daughters of Israel, Introduction, p. 15

In conclusion of the Halacha: In a place where women are accustomed to reciting a beracha on a positive time-bound mitzva, one should rule for them that they continue to recite it. In a place where the custom is unclear, it is desirable to rule for those who ask [that they should] not recite a beracha, but one should not protest at all women who recite aberacha, or anyone who rules for them that they should recite a beracha.