Search vcoins. Searching Ma-shops may also help but I don't recall if the dealers on there do much much with Byzantine.
https://www.ha.com/c/search-results...ne+constantine+IX+gold&ic10=ArchiveTab-071515 Look to be in the $230 range each 25 years ago. If I had to guess that would be 10x spot back then. The similar Michael VI coins sold more recently with same weight appear to realize much much more, so I will assume they are much rarer.
Michael VI reigned for a year. Michael VII reigned for seven, but he also had increasingly poor gold content in his coins, allowing him to strike more of them.
Yup. According to my spectrometer, the Constantine coin is close to 22kt, and the Micheal VII is 14kt.
After quickly checking CNG, it seems that Michael VII mostly sells for around $300. Some sell for more, some less, but that seems to be a median.
Feel better soon! I can let you come to your own conclusions on the price. Your Constantine IX is a later one, struck from 1049-1053.