This, without any questions is my favourite Greek Royal Tiara!
The tale of this tiara begins with the giant emeralds it houses. Sixteen-year-old Grand Duchess Olga Constantinova of Russia brought a magnificent set of cabochon emeralds in varying sizes with her when she married King George I of Greece in 1867.
In Queen Olga's day, the emeralds were separate pieces and she wore them as such, pinning them to her dress and kokoshnik, and hanging them from her necklace and so on. It wasn't until their next wearer, Queen Elisabeth of Greece - her husband, King George II, was Olga's grandson and inherited the emeralds after her death in 1926 - took possession that they began to take the shape of the set we know today.
Even then, it was a slow evolution in design. She wore a single emerald across her forehead as part of a leafy bandeau, as was the fashion at the time, and she wore multiple emeralds upright on a band of diamonds. Eventually, she had Cartier make her a kokoshnik-style tiara which uses 5 of the emeralds in between mirrored diamond "E" shapes - "E" for Elisabeth, naturally - with a band of diamonds surrounding the whole configuration. It's very close in form to a tiara owned by her sister, Queen Maria of Yugoslavia, so perhaps she had a little inspiration. Queen Elisabeth and King George II went through a period of exile (the Greek monarchy doesn't exactly have a history of stability, you see) and ended up divorced with no children. The customized "E" tiara stayed with the Greek family, though, and we next saw it worn by Queen Frederika, wife of King Pavlos I, younger brother of George II.
By the time Frederika wore it, the tiara had changed yet again into the design we know today. The band around the top and edges had been removed. Frederika preferred to use the tiara as a necklace, often in combination with the massive Queen Sophie's Diamond Tiara that we just saw reappear. On Frederika, we also see the final parure which put the rest of the set of cabochon emeralds to use.
The parure consists of the tiara (which has 5 emeralds), a pair of earrings with emerald drops, a brooch made of more diamond "E" shapes and emeralds, and 5 independent emerald drops which can be suspended from the brooch. When Princess Anne-Marie of Denmark married Frederika's son King Constantine II, Frederika handed the emeralds over to the new queen.
In contrast to her late mother-in-law, Queen Anne-Marie uses the tiara as a tiara, not a necklace, and makes up a necklace to go with by suspending varying numbers of emerald drops or the entire emerald brooch from a diamond necklace. She often uses a necklace given to her by her mother, Queen Ingrid of Denmark, for this task. The necklace comes from Anne-Marie's grandmother, Queen Alexandrine, and was initially a longer piece. Ingrid split it in two, and gave one part of Anne-Marie and one part to her sister Benedikte.