There are a lot of different kinds of parchments, ink, seals etc. around and what might work for one would be dangerous overkill for others. The previous poster's advice would be towards the "strenuous" end of the spectrum, and one that I personally would not do.
I have had good results humidifying gently with Gore-tex (available from Talas) and then stretch drying. The table top is misted with deionized water, the Gor-tex lain over that, the parchment placed face up on the Gore-tex, and covered with Mylar, so that I can keep an eye on the inks etc.
When humidified ( and this can take from 5 minutes to an hour, depending on the above variables) I remove the parchment to dry, clean table top, place strips of 8-ply laminated to Coroplast (These are 2" wide and of varying lengths) around the perimeter, and weight. My weights are lead shot in small mason jars, everyone has their own system, but they have to be heavy.
This might take 3 times repetition or so, go slow and easy is the motto. It is not a huge problem to repeat the process, but if it goes too far there is no going back.
This general system has worked for parchments from 1450 - present, though there will always be exceptions to the rule that one should be alert for.
Hope this helps.
Rebecca