Is a woman allowed to freeze her own ova if she is coming to the later years of her life and is afraid she will miss her opportunity to have her own children naturally or otherwise, or is that frowned upon in Halacha?
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The worldwide experts in fertility and halacha are Machon Pu'ah. They have a questions & answers section on their website.
According to Rabbi Elhanan Lewis (link) it is permissible with halachic supervision.
I second the opinion to ask your local rabbi, and I think it is relevant to draw your rabbi's attention to Machon Pu'ah.
I'd assume it's permitted if the woman wanted it.
Extracting and freezing the cells
I know the similar question was asked regarding taking a man's sperm and freezing it so he might still be able to father a child after, say, treatment for testicular cancer.
Philosophically it's permitted, though not required (nor particularly advocated; patient's own decision). The mitzva of Pru Urvu covers only marrying someone believed to be fertile, and going about normal life.
The concerns for a man have to do with some halachically objectionable methods of extraction.
In a woman's case, the extraction isn't halachically prohibited other than that the process can be taxing on the individual and, as it involves some surgery, contains a small amount of risk. My strong sense is that the need here far outweighs the costs, if that's the patient's choice.
What about faith?
The last question is a philosophical one: it's one thing to bank reproductive cells if, say, the patient is about to have cancer treatment that could be sterilizing. We know there's a problem, so G-d gives us permission to use medical technology to treat it. In the case of a woman who just can't find a decent husband, should we say she should have faith rather than go through long and arduous processes?* My guess here is that the process isn't that bad, and the risk of not finding a husband in time are (sadly) non-trivial enough that it would be justified, if that's what this woman wanted to do. Again it would be wise for her to discuss the idea with a counselor and spiritual advisor, to see if this would really improve her life.
*If genetic testing was a long and arduous process, and its outcome useful only in rare cases, Rabbi Moshe Feinstein wrote that people of faith shouldn't do it (however that's not the case; go get tested for Tay Sachs and the like!)