Stabilization of a circular saw blade is provided, through use of a blade stabilizer mounted adjacent a workpiece in a fixed relationship to the workpiece and having a stabilizer contact element adapted to bear against the circular saw blade and exert a force against the saw blade in a direction substantially perpendicular to a cutting plane of the saw blade at a point on at least one of the blade faces on the working side of the blade, proximate an axis of motion passing through an axis of rotation of the saw blade and the workpiece in the cutting plane, as the circular saw blade and/or the workpiece move relative to one another along the axis of motion. The axis of motion may be linear or curved. Some embodiments include additional blade stabilizers.