Zircons are fine with soap and a toothbrush but NOT emerald. If they’ve been oiled (very common) or have surface reaching fissures (also common), no soap. I just use plain water and very gently clean. No ultrasonic cleaning either for emeralds (or pearls or opals!)
I bought the emerald 6 years ago and may have scrubbed it down with soap a few times! Will not do that anymore! I didn't think of that! I have been babying the zircons like anything because I liked their settings so much!