A quantitative frequency-domain model of induction-based magnetoreception is presented for elasmobranch fishes. We show that orientation with respect to the geomagnetic field can be determined by synchronous detection of electrosensory signals at harmonics of the vestibular frequency. The sensitivity required for this compass-sense mechanism is shown to be less than that known from behavioral experiments. Recent attached-magnet experiments have called into doubt the induction-based mechanism for magnetoreception. We show that the use of attached magnets would interfere with an induction-based mechanism unless relative movement between the electrosensory system and the attached magnet is less than 100 mum. This suggests that further experiments may be required to eliminate induction as a basis for magnetoreception.