Terahertz metamaterial structures that employ flexing microelectromechanical cantilevers for tuning the resonance frequency of an electric split-ring resonator are presented. The tuning cantilevers are coated with a magnetic thin-film and are actuated by an external magnetic field. The use of cantilevers enables continuous tuning of the resonance frequency over a large frequency range. The use of an externally applied magnetic field for actuation simplifies the metamaterial structure and its use for sensor or filter applications. A structure for minimizing the actuating field is derived. The dependence of the tunable bandwidth on frequency is discussed.