Methods of operation of an induction melter include providing material within a cooled crucible proximate an inductor. A desired electromagnetic flux skin depth for heating the material within the crucible may be selected, and a frequency of an alternating current for energizing the inductor and for producing the desired skin depth may be selected. The alternating current frequency may be adjusted after energizing the inductor to maintain the desired electromagnetic flux skin depth. The desired skin depth may be substantially maintained as the temperature of the material varies. An induction heating apparatus includes a sensor configured to detect changes in at least one physical characteristic of a material to be heated in a crucible, and a controller configured for selectively varying a frequency of an alternating current for energizing an inductor at least partially in response to changes in the physical characteristic to be detected by the sensor.