One good way to make a box with a perfectly fitted lid is to build that box like a solid cube and then separate the lid from the box on the tablesaw. Although this works pretty well there can be a problem at the corners where there's a slight "snipe" to ruin it. Several methods can be used to overcome this like trying to place a spacer the same thickness as the kerf so that they won't squeeze together at the end of the cut but that is iffy at best! I had read somewhere to cut partially through the box and then finish it off with a utility knife, thought that would leave a sliver which could potentially ruin the edge. Here's what I did and the results. These boxes are about 11" x 27". The first thing I did was to set the fence and then adjust the blade so that it left about 1/32" of the side. I didn't measure this, just eye-balled it. Then I cut the 11" ends first. Now I raised the blade to just cut through completely and ran the long sides. Hard to tell from this picture but that's what it looked like.
Next thing I did was to take a thin piece of wood and place it into the box near the ends as a "kerf keeper". This allowed me to use a flush cut saw to complete the cut. You can see the small section that remained.
The final step was using a low angle block plane to smooth the edge. I set it for a very thin cut, planed with the grain, and also skewed it towards the end to avoid tearing out the outer edges. All that remains to be done is knock down the edges and we're good to go -- give it a try!
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