The Shulhan Aruch (Siman 303) records a Gezerah (Rabbinic decree) from the Gemara, prohibiting women from wearing jewelry in the public domain on Shabbat. The Hachamim were concerned that she might remove the jewelry to show a friend, and inadvertently carry it in the public domain. Some Rishonim extend this Gezerah to apply to a courtyard, as well. The Rashba even prohibits wearing jewelry inside the house, as she may accidentally walk out of the house wearing the jewelry.
The question is whether this Gezerah applies today. The Shulhan Aruch clearly states that, despite the Gezerah, the common custom was for women to wear jewelry in the public domain. One explanation for this deviation from the Talmudic Gezerah is that our public domain does not constitute a "Reshut Harabim D’Oraita"- A Public Domain, as defined by the Torah, which must be similar to the context of the Jews in the desert-more than 600,000 people passing through in one day. Our public places do not have such a population.
The problem with this justification is that the Shulhan Aruch himself rules, later on, that the amount of people is not a factor in determining a "Reshut Harabim." Rather, it is the width and configuration of the streets which define it. How can Maran use a leniency that he, himself, does not agree with?
Hacham Bension in his Or Lesion (Vol. 2) deals with this apparent contradiction. He offers a convincing explanation: Indeed, Maran is stringent and holds that a public domain can be a Reshut Harabim, even without 600,000 people. However, that is only with regard to actually performing the prohibited act of carrying. In this case, the woman is not actually carrying the jewelry; she is wearing it. The only issue is the Rabbinic Gezerah that is concerned she may take it off and carry it. Regarding a Rabbinic concern, Maran is lenient and adopts the opinion that our streets do not constitute a Reshut Harabim.
In fact, the consensus of all the Poskim is that there is no problem for a woman to wear Jewelry in the public domain. This is the opinion of Hacham Ovadia (Hazon Ovadia), Hacham Bension, and the Menuhat Ahaba. Of course, she must be extra careful not to remove it, and if she does, she must remain in her place and not continue walking. This is particularly relevant to an engagement ring, which is commonly removed and shown to friends. Interestingly, all of the Poskim add that if one is stringent and refrains from wearing jewelry in the public domain, she is worthy of blessing.
SUMMARY
There is a Halachic basis for women to wear jewelry in the public domain on Shabbat, as long as they are careful not to remove it. However, those who refrain from doing so are praiseworthy.
