Hot tip from the comments portion of the blog: Robert Montgomery should be showing up on What's My Line on GSN in October sometime:
Episode #345, first aired: January 13, 1957
Game 1: Muriel Fleit, Mary Barber & Myrtle Berne (as Mystery Guests and the panel is blindfolded) - "Secretaries to Arlene Francis, Bennett Cerf & Dorothy Kilgallen)" (salaried; they won $50)
Game 2: Robin Roberts - "President of Frozen Shrimp Company" (he is the President of the Gold King Frozen Shrimp Co; he is also the pitcher of the Philadelphia Phillies baseball team; from Philadelphia, PA; he won $50)
Game 3: Robert Montgomery (as Mystery Guest) Bennett Cerf guessed his identity at $25
If you're really good at figuring out the current episode playing vs. the order 345 is in, you can figure out the air date on GSN. I'm not that talented...
A kind thank you to the tipster!