I learned to do borders a bit like most folks and it works with out waves. I pat out the quilt top, not stretching it. I place the borders on top of it, measuring the long sides first. I also pat out the borders with the quilt again so they are even and not stretched. I then cut the borders to fit the quilt top.
I then fold the top in 2, putting a pin in the middle of the side, then taking each corner placing it on that pin, pinning the side in quarters. I do the same for the other side and for both cut borders. Then I match up the pins on each quilt side with the pins on the border. That way, you know if you have to ease anything in or not. I do not have wavy borders and they turn out great.
The teacher I have (still take weekly classes at the local tech college) is a master quilter and she taught me this way. Try it, you have nothing to lose.