A method for operating a refrigerator appliance includes operating a dispenser of the refrigerator appliance to initiate a flow of liquid water or ice into a container positioned within a dispensing recess of the dispenser in response to a user input at a user input panel of the refrigerator appliance, receiving one or more signals from a sensor positioned at the dispensing recess after operating the dispenser to initiate the flow of liquid water or ice into the dispensing recess, and detecting a presence of the container in the dispensing recess based at least in part on the one or more signals from the sensor only after operating the dispenser to initiate the flow of liquid water or ice into the dispensing recess. A related refrigerator appliance is also provided.