In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Answering your question, the late Saudi scholar, Sheikh Ibn Baz (may Allah have mercy on him) stated:
If a necklace, for example, has both gold and these other stones, the woman, her husband or guardian then must ponder the matter and try to estimate the amount of gold or give it to an expert to estimate it. It is sufficient to be fairly certain about the matter [and one need not be exact].
If the amount of the nisab is reached, Zakah must be paid. The nisab is twenty mithqaals.. which is ninety-two grams.
Zakah is to be paid every year [once a year]. The amount is 2.5%. For example, on one thousand, a person pays twenty-five.
This is the correct opinion among the views of the scholars. If the jewelry is for business purposes, then one pays Zakah on all of it, including pearls and diamonds, according to their [market] value, which is the same with all types of merchandise goods. This is the opinion of the majority of the scholars.
Almighty Allah knows best.
Source: Islamic Fatawa Regarding Women, Compiled by Muhammad Ibn Abdul-Aziz Al-Musnad and translated by Jamal Al-Din Zarabozo, Darussalam, 1996.