We present an experimental realisation of two new artificial microswimmers that swim at low Reynolds number. The swimmers are externally driven with a periodically modulated magnetic field that induces an alternating attractive/repulsive interaction between the swimmer parts. The field sequence also modulates the drag on the swimmer components, making the working cycle non-reciprocal. The resulting net translational displacement leads to velocities of up to 2 micrometers per second. The swimmers can be made omnidirectional, meaning that the same magnetic field sequence can drive swimmers in any direction in the sample plane. Although the direction of their swimming is determined by the momentary orientation of the swimmer, their motion can be guided by solid boundaries. We demonstrate their omnidirectionality by letting them travel through a circular microfluidic channel. We use simple scaling arguments as well as more detailed numerical simulations to explain the measured velocity as a function of the actuation frequency.