Comments because of questions 
- the 14th century lampas/brocade is possible dyed with indigo and mignonette (yellow)
- I do not know if they would weave 15th century patterns also, ask them 
- the 13th century samit is also dyed with natural dyes (possible also mignonette)
- also the silk core thread which is covered with gold is dyed!
- the pictures on the page show the original cloth the replica is based on, of course the re-weaves will look newer, unworn, brighter, without flaws.
You can find the originals in:
Mittelalterliche Seidenstoffe. Leonie von Wilckens. Staatliche Museen zu Berlin, Bestandskatalog XVIII des Kunstgewerbemuseums. Berlin, 1992.
( http://www.amazon.de/Mittelalterliche-Seidenstoffe-Jahrhunderts-Berliner-Kunstgewerbemuseum/dp/3886090795 )
I do not know if there is a translation.
The show owners can speak english. please contact them for questions- I onlx try to spread this, because a basic number of orderers is needed for the cloth to be woven, and I also want some 
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Diu Minnezīt
Reconstruction of textiles, armour and daily life
1250,1350,1475
Nuremberg and Paris
http://www.diu-minnezit.de
IG Meisterhauw
Reconstruction of late medieval and early renaissance fencing techniques
http://www.meisterhauw.de
Nuremberg in the middle ages
http://www.nuernberg-im-mittelalter.de