Yes, I'm sure they had 'panes of glass,' especially large ones, during that period...
http://www.shadowshroud.com/faq.htm#faq9
2. The Glass Questions
a. How big was medieval glass? Could they make big pieces, or were they all little like those in stained-glass windows?
Wilson’s answer:
When I first presented the Shadow Theory, tentatively, to the student body of New St. Andrews College, I did not know the answer to this question. A member of my audience, however, did. As she had worked a great deal within an artisan glass shop that still used medieval technique she was able to describe the method for blowing a sheet and told me that sheets measuring 6’x8’ were fairly common. When I looked into her explanation, before experimenting, I found that she was absolutely right. Throughout the thirteenth century glass blowers were capable of creating large sheets. They would blow cylinders, up to nine feet or more in length and then, while the glass was still molten enough, they would cut off the bowls that formed both the top and the bottom and slice the cylinder lengthwise, unfolding it into a sheet. The sheets would be cut into small pieces for use in leaded stained-glass windows, or painted while large.
As the Shroud is roughly fourteen feet in length, two pieces of glass would be necessary, both at least six feet long. The image of the front of the man would be produced beneath one and the back of the man beneath the other.
When Dr. Antonio Lombatti, Fellow Researcher in Medieval Church History at the Deputazione di Storia Patria in Parma, Italy was recently asked about the availability of glass large enough to produce the Shroud, he responded, “Of course a medieval artist could have enough glass to produce that relic.” He pointed out that six foot painted glass windows were not uncommon, and also mentioned that the length discrepancy between the front and back images of the man in the Shroud (1-2 inches) suggests two different phases of production.
Its amazing how some con artist back in the Middle Ages still has all the scientists stumped.