The way I interpret Hermione thus far is as a very strong female character. She convinces Polixenes to stay longer where her husband could not, stands up for herself and for Polixenes’s wife when he seems to speak ill of women, and stands up for herself against her husband. She seems sassy and sarcastic, and thoroughly able to hold her own against the male characters of the play.
In Act I Scene II, she pretty much threatens (not entirely seriously) to keep Polixenes in Sicilia as a prisoner if he refuses to stay as a guest, and asserts that “A lady’s ‘verily’ is as potent as a lord’s” (50-51), matching her use of the word against his. This section of text shows her off as assertive in general terms of her ability to convince him, and in her willingness to verbally spar with him. The fact that she explicitly says that a woman’s word is just as good as a man’s, though, sets her up further as a strong female character and defender of women. She also does not speak in terms of herself, saying her “verily” is as potent as his; she speaks for “a lady” in general, which I think is much more telling of her character and her belief in her gender as a whole.
In the same scene, Polixenes implies that women are temptresses who lead men into sin, saying “Temptations have since then been born to’s” causing both he and Leontes to “trip”, or sin, the “temptations” specifically referring to Hermione and Polixenes’s own wife (75-80). Hermione interrupts him, saying “Grace to boot! / Of this make no conclusion, lest you say / Your queen and I are devils” (80-83). She, again, verbally spars with him and somewhat jokingly points out that he’s saying something offensive to her and his own wife, basically telling him not to finish what he’s started to say. Also yet again, she does not only defend herself, but includes his wife, this time making things more personal than speaking generally of all women as she did when she asserted that a woman’s word has just as much worth as a man’s word. This reminds me of some contemporary arguments (that are surrounded by some controversy) that men should respect women because they would want others to respect their wives, mothers, sisters, or daughters (thinking of women in relation to themselves as opposed to as human beings that deserve respect independently of their relationships to men). Despite the modern controversy, this type of personal argument, especially in such a world dominated by patriarchy, works in terms of garnering some kind of respectful treatment toward women.
Hermione also stands up for herself when her husband implies, pretty much, that she’s good for nothing. Leontes says, “Hermione, my dearest, thou never spok’st /To better purpose,” and she replies, “Never?” to which he answers, “Never but once” (1.2.85-90). Her response to this, the way I interpret it, is sarcastic and sassy: “What, have I twice said well? When was’t before? / I prithee tell me. Cram’s with praise and make’s / As fat as tame things.” (1.2.90-92). She is challenging her husband for saying that she’s only said or done anything of worth once before, (to me) mockingly (although lightly so) begging him to tell her what her previous achievement was, and fatten her up with praise, as if a single “compliment” would accomplish that. She also references her earlier “Grace to boot!” comment to Polixenes, saying of her first “good deed,” “Oh, would her name were Grace!” (1.2.97-99). The footnotes of the Norton suggest that “[she] may be countering Polixenes’ earlier suggestion that she first caused Leontes to sin” (3137), which is an interpretation I like because it goes along with the idea that she’s defending herself and women against the men’s misogyny.