We present experimental results on the stability of a free liquid metal surface influenced by an alternating magnetic field. The field is generated by an inductor fed by a high-frequency electrical current. The experimental setup consists of an annulus filled with the liquid metal galinstan. We observe three kinds of instabilities: exciting of capillary waves, a static high-amplitude surface deformation, and eventually an electromagnetic pinch at a critical inductor current I(cp). The data show that I(cp) correlates directly with the current frequency and the geometric parameters.