The best martini glasses are not martini glasses. They were originally designed one or two centuries ago as champagne or sherbet glasses and were adopted as a cocktail glass in the early 1900s.
My favorites are Seneca cut crystal. The
Seneca Glass Company existed from 1892 to 1983 and made crystal for the White House, the rich and celebrities. If you want Seneca crystal today you will have to search places like eBay and
Replacements Ltd. Try search terms "champagne" and "sherbet" in addition to "cocktail." The champagne stem is often slightly taller than the sherbet stem and larger than the "cocktail" glass. Either can work but I prefer what I think of as the classic martini glass with longer stems and a triangular profile. Even so, some of the martini glasses in my collection have curved sides, shorter stems and even no stem but always a dramatic form.
Despite all the images and links on this page, I don't have a financial relationship with Replacements, Ltd. However I've bought a lot of crystal from them. They are a great source. When they have a sale, you can buy the finest cut crystal for about the same price as cheap glass anywhere else.