This is really a bigger question than just these two documents. More generally how were books and documents written in the pre-typewriter age? I assume they used something to keep lines even and straight.
So, when we say that Jefferson wrote the Declaration of Independence, we don't mean that it's his handwriting on the final copy. The actual application of ink to paper for official and legal documents was left to professional calligraphers, called engrossers. Timothy Matlack seems to be credited as the engrosser of the Declaration, while the Constitution was engrossed by one Jacob Shallus. The National Archive has a bit on the engrossing process and its complications.