The Roman period saw the invention of glass blowing around 100 A.D. This new technology allowed thousands of glass bottles to be produced and made bottles more accessible for medicine and perfumes. The tear-drop shape was easily produced and quickly became a common style. More information on apothecary bottles can be found at the Glass Museum.
The confirmed use of bottles during this period by apothecaries lends credibility to the argument that lachrymatory were actually never used to capture tears. The problem with this argument is the reference to capturing tears in the Bible. Regardless of the version or interpretation, it is clear that the concept of capturing tears existing in the popular culture of the time.
Roman lachrymatory are available through a variety of antiquities dealers and auction houses. More info on these pieces can be found in the collecting section.
Interestingly, the art of glass blowing was largely lost, along with many other things, during the Dark Ages. An interesting perspective on why the Dark Ages began is offered by Professor Mike Baillie. Unfortunately, the tear bottle tradition was also lost for a millennium.