Yes—the 3 engagement rings on are list are all machine-cut. CZ has a rating system which comprises of 5 levels—with each one being determined by an “A”. This means the lowest quality is 1A (or a simple “A”) while the highest quality is 5A (AAAAA”).
With most of the options above, that’s a hardness of at least 8.3 which is considered almost as hard as diamonds.
So choose something along these lines. Though, if you want to choose 5A stones, the hike in price should not come as a surprise.