In 1992, then-commander Jim Sena ordered a contest within Squadron 36 to create its own squadron patch. After several entries, Sean P. San Filippo's design was selected. With minor modifications, the insignia was created as shown above. The insignia's parts were chosen as the following:
- - - Name. Across the top of the patch is the name “John J. Montgomery,” who is the aviation pioneer for whom our squadron is named.
- - - Eagle. Predominantly displayed on the right side of the patch is the bald eagle, which represents the United States of America and the aviation superpower that we are.
- - - Olive Branch. Clutched In the talons of the eagle is an olive branch that symbolizes the peaceful, benevolent ideas that the Civil Air Patrol is founded upon.
- - - Border. The black border represents the squadron colors.
- - - Earth. The earth represents where we came from.
- - - Moon. The moon represents where we have gone.
- - - Stars. The stars for where we are heading.
- - - Motto. Across the scroll are the words “Exceed the Challenge.” This is the squadron motto and the idea on which senior and cadet members strive.
- - - “36.” The large “36” in the upper left-hand corner represents the squadron’s informal numerical designation.
- - - Yellow. The yellow color represents the torch of knowledge that our cadets strive for.
- - - Scroll. The scroll represents camaraderie between senior and cadet members.
- - - White. The white on the patch stands for the pure eagerness of youth, striving for knowledge.
The manufacturer of these insignia is not known, although currently-unsubstantiated stories imply that these insignia were made in Korea.