
Stem glass. Gilt and enameled blown cristallo glass, Venice, late 15th–early 16th century.between circa 1575 and circa 1625 collection of Giampietro Campana di Cavelli; : purchased 1974 Louvre Museum, Paris, France. Source
The 16th century was the golden age for Venetian glassmaking in Murano.At least 28 glassmaking furnaces were in Murano in 1581. Collectors of Murano glass included Henry VIII of England, Pope Clement VII, King Ferdinand of Hungary, Francis I of France, and Phillip II of Spain.
The glass makers were so popular that this Cristallo method of glass making developed into the word we use in English today as “Crystal”
Another word for this Italian glass was “crystalline” which Shakespeare uses in his play Cymbeline to describe the material out of which Jupiter builds his palace. (Act V Scene 4) FUN FACT: There’s a real Cymbeline Castle location in England.
Glass history (yes that’s a real area of history) credits English glass merchant George Ravenscroft with the creation of the “Crystal” as we know it today– a clear glass he called crystalline—but it was not stable. Three years later, in 1676, he improved this glass by adding lead oxide, and lead glass (a.k.a. crystal) was created. This late 17th century version of crystal glass is the “crystal” as we think of it today, but the term applied to glass creations during Shakespeare’s lifetime as well, and it was during Shakespeare’s lifetime that the word “Crystal” came to prominence.
Despite lead glass not being created until the late 17th century, the mineral has been called “crystal” since Anglo-Saxon times; it was regarded by the ancients as a sort of petrified ice. And the word “Crystal” was used As a shortened form of crystal-glass dates from 1590s. It was used As an adjective, from late 14c.
So Shakespeare has some precedence for including it in his plays, that could date back to any number of the very old history sources he is known to have used when writing his works, but intriguingly, a fascination with glass, and specifically the Italian glass, also appears to be a slice of Shakespeare’s contemporary culture as well.

Italy, Venice, circa 1550-1650Furnishings; ServicewareColorless, free-blown and pattern-molded cristallo glass.Gift of Mr. and Mrs. Eric Scudder, Miss Bella Mabury, Dorothy S. Blankfort, Mr. and Mrs. Jerome K. Ohrbach and others (M.85.150.15) Source

Example of a Scottish Quaiche by Robin Wood. maple and silver. Source
At this point, different craftsmen started to create different styles of quiach, slowly changing the style of the handles and, over time, changing the form of the glass entirely. Eventually, craftsmen would use lighter and darker woods, which created patterns on the cups, and eventually, they began embellishing the cups with silver. Every craftsmen would create something totally unique, in an attempt to capture the imagination of those who bought and used the quiaches.
The silver quiaches were eventually engraved with patterns, and in some instances even designed to replicate the appearance of wood. The bowls became statement pieces, and played an important role in the social gatherings that usually accompanied whiskey drinking. During the 17th Century, a “quiachfull” of whiskey –enough for one gulp – was served once at the beginning of a social event, and once at the end. Source
Suprisingly, this quaiche that was used in Scotland for whiskey was, in England, the design of the low bowls used for bleeding a patient for illness.
Traditionally quaichs are made of wood, an artform known as “treen”. Some early quaichs are stave-built like barrels and some have alternating light and dark staves. The staves are held together by bands of willow or silver. They generally have two, and more rarely three or four, short, projecting handles. Other wooden quaiches were lathe-turned out of a single piece of wood and there was another group which were turned then carved outside in basket-weave pattern. In addition to wood, they are made of stone, brass, pewter, horn, and silver. The latter were often engraved with lines and bands in imitation of the staves and hoops of the wooden quaichs. (Source)
So it seems that while glass vessels, and even glass drinking vessels were in existence during Shakespeare’s lifetime, it is far more probable that the bard used a wooden (or perhaps leather?) drinking cup whenever he enjoyed a dram of ale, and not a glass one.