A method of verifying swelling of a swellable material in a well can include connecting a transmitter to a sensor which senses a parameter indicative of degree of swelling of the swellable material, and conveying a receiver into an interior of a tubular string. The transmitter transmits to the receiver an indication of the degree of swelling of the swellable material. A packer swelling verification system can include a swellable material which swells in a well, and a well tool which is conveyed to the packer in the well. The well tool receives an indication of a degree of swelling of the swellable material. A method of verifying whether a swellable material has swollen in a well can include positioning a conductor proximate the swellable material, whereby the conductor parts in response to swelling of the swellable material, and detecting whether the conductor has parted.