The pilot of a Boeing PT-13B Stearman reported that after conducting maintenance on his airplane, he taxied to the run-up area to conduct an engine run-up. With the airplane being a tailwheel-type configuration, he made continuous S-turns to ensure visibility ahead of his position. While approaching the run-up area, during a turn to the right, he observed an airplane on the runway. He reported that he was “clear” in front of the airplane and he continued his S-turn to the left. During the turn, the Stearman collided with a Cessna 172M. The pilot of the Stearman stated that he did not see the Cessna prior to that final turn when he saw its empennage. The pilot of the Cessna 172M stated that he was stopped in the run-up area conducting a run-up when he looked to the left and observed the Stearman adjacent to the end of the Cessna’s left wing. He stated that the Stearman taxied forward and the propeller struck the left wing, resulting in substantial damage. Neither pilot reported mechanical failures or malfunctions with their respective airplane’s airframe or engine prior to the accident.