The symbolism and meaning of Juliet giving Romeo a ring, as expressed in the line, "O, find him! give this ring to my true knight," is actually very interesting because it actually defies tradition (III.ii.147). In Renaissance England and Italy, a ring was exchanged at the point of betrothal. The betrothal was a ceremony held in which the couple sealed their intentions to marry, as well as the rights to transfer possessions. Certain symbolic actions took place that later became part of the wedding ceremony, such as the man giving his fiancee a ring and a kiss, as well as the man joining hands with his betrothed's family in order to symbolize the right to acquire her possessions from her father. However, the betrothal ceremony was not the actual wedding ceremony and no physical union could take place before the actual wedding ceremony. It was not uncommon for couples to sometimes have to wait years before the actual wedding ceremony (Thomas, "Medieval and Renaissance Marriage").
Hence, there are two things that are interesting about Juliet sending Nurse with a ring to give to Romeo because this action defies tradition in two ways: 1) Their wedding ceremony has already taken place and an exchange of rings was not a tradition for the wedding ceremony at this time. Instead, the exchange of a ring was a tradition of the betrothal ceremony and symbolized the prospective groom's rights to the bride; 2) It was actually the man who gave the woman the ring, and not the reverse, as Juliet has done.
Therefore, Juliet's action seems to symbolize rebellion. Juliet is rebelling against her parents as well as social norms. Juliet knows very well that her parents have not given Romeo the rights to her, but one thing she is saying is that it does not matter to her--she has given herself away instead. Through this action, Juliet is also symbolically claiming Romeo as her own "bride." A bride was considered socially weaker than a husband, and everything the bride owned belonged to the husband. Due to his banishment, Romeo certainly is now the weaker member of the couple--he no longer has any inheritance or any worldly possessions to share with either a bride or a metaphorical "husband." Juliet is now the one who still has worldly goods and a chance at inheritance. Therefore, in claiming Romeo as her metaphorical "bride," she is bestowing the promise to take care of him in the same way that a husband would be legally responsible for taking care of a wife. This would be an act of social rebellion because, due to his banishment, Romeo would not socially be seen as either a worthy and valuable husband or "bride" for anyone to have. Therefore, Juliet is symbolically saying that she does not care what society thinks of Romeo.
Hence, Juliet giving a ring to Romeo not only symbolizes an act of unity and love, it also symbolizes an act of rebellion because a ring was not something that a woman gave a man.