Popcorn machines having radiant burners and associated systems and methods are disclosed herein. In one embodiment, a popcorn machine includes a kettle assembly having a heating plate that separates an upper portion from a lower portion. The heating plate can include a coated lower surface to absorb radiant heat, and the kettle assembly can be supported by a base having a gas-fired radiant burner. The radiant burner can include a heating element positioned to direct radiant heat toward the heating plate. In several embodiments, the heating element includes an opening extending therethrough, and a coupler can extend through the opening to connect a motor in the base with a mixer in the upper portion of the kettle assembly.