Why does paper buckle anyways?
The paper expands when wet and then shrinks when dry. Cheaper watercolor paper is not made of cotton it is actually made of wood pulp and the fibers are shorter, and not as strong as cotton so it will buckle a lot more. It makes your paint dry unevenly and the pigments are less vibrant and more muted on wood paper.
So here is a tip. BUY 100% COTTON WATERCOLOR PAPER

Cotton fibers are longer and stronger and cotton paper buckles less but it will still buckle with enough water.
HOW CAN YOU PREVENT BUCKLING PAPER
So the watercolor paper industry came up with watercolor blocks where the paper is glued down on all 4 sides except a small 1-inch area so you can run a knife under the edge to free the paper once your project is dry.
So does that mean watercolor blocks are pre-stretched? I can attest to they are NOT pre-stretched and if you throw a lot of water on it it will indeed buckle but once dried being held down on all 4 edges does help with the buckling...but not completely wrinkle-free.
You can use a heavier paperweight. The most popular weight is 140 lbs but if you are working very wet on wet techniques you may want to try 300 lb paper. It will hold more water without buckling but is still not foolproof and is more expensive.
You can stretch watercolor paper by soaking the sheet in clean water for a few minutes and taping and stapling your paper down to an artboard and letting it dry. The expanded wet paper when it shrinks will be tauter due to the tape and staples keeping it from moving. Therefore pre-stretched preventing the buckling....
The problem is with this solution is that it is painstakingly slow, you can damage the paper, and accidentally remove the sizing which is hugely important to watercolor paper.
Most importantly it is basically a huge pain in the ass. It is a messy job, time-consuming, and you have to wait for it to completely dry.... who has time for that!
You can tape down your paper without wetting it in order to prevent some buckling.
But the only foolproof way is to flatten paper after you are done with your masterpiece!
FLATTENING OPTIONS
You can mist the back of the watercolor paper and place a towel over top with heavy books on top of the paper for a day. So this is a bit messy and a bit more work so screw that!

The best and easiest way in my opinion to flatten your curled watercolor painting is to just iron it! Yes, good watercolor paper after all is 100% cotton.
Have a clean neutral barrier between the ironing board your work and the top of your work. Sandwich your painting between two cotton sheets. Set your iron on cotton and steam and take 10 seconds to give a few quick puffs of steam and move your iron over top your project to flatten it.

Of course, if you were to leave your iron in just one area for too long chances are you may scorch the paper but anyone who knows how to use an iron and has ironed clothes knows this....and if you don't I am telling you now:)
Then place some heavy books on top and leave it for a few hours.
Conclusion
I try to prevent buckling as much as possible by picking the best paper for the job, taping down my watercolor projects to a board if I am not using a block to do my work and that is it!! After my project is done and dry I remove the tape then iron it!
Paint, iron, repeat it is that simple.
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