Measure the width of the new threshold. Transfer this width measurement to a piece of hardboard. Rip the hardboard with a circular saw. Cut a 12-inch piece off the ripped hardboard.
Set the hardboard in the door opening, where the new threshold will go. Press the hardboard tightly against one of the side jambs. Open a compass to the largest gap between the side jamb and the hardboard.
Trace along the hardboard's edge, following the jamb's contours. Cut the hardboard along the traced line using a jigsaw. Test fit the hardboard against the jamb. Make any necessary adjustments to make the hardboard fit tightly around the jamb's contours.
Lay the new threshold on a flat surface. Set the hardboard on top of the threshold, lining up the contoured end with one of the threshold's end. Trace around the contoured hardboard's end with a marker. Flip the hardboard upside down and place it on the threshold's other end. This creates a mirror image for the side jamb on the opening's opposite side. Trace around the hardboard's contours.
Cut the threshold along the marker lines with a jigsaw. If you have a metal threshold, smooth the cut edges with a metal file. If you have a wood threshold, smooth the cut edges with a rasp.
Test fit the new threshold in the door opening. File away any rough edges that get stuck on either side jamb with either the metal file or the rasp.