Jardin came in sixth with a time of one minute, 57.92 seconds, which was 0.76 seconds behind first-place finisher Federica Pellegrini from Italy.
Cheverton touched in at 1:58.11 to place ninth in the heat. The top 16 swimmers advance.
Both Canadian swimmers are making their Olympic debut in London.
Rising American star Missy Franklin also qualified with the third-fastest time of 1:57.62.