Electromagnetic field actuated flows within microchannels is of significant importance in the field of microfluidics. In the present work, a mathematical model is derived for the micro scale electroosmotic Couette flow under the influence of combined electromagnetic field. Combined effects of longitudinal and lateral electric fields along with vertical magnetic field are taken into account while solving the governing equations of fluid flow. Velocity profiles under the varying influence of parameters like electromagnetic force and electroviscous number are shown. The overall flow rate enhancement in the presence of electromagnetic effect is noted up to the value of Hartmann number (Ha) = 1.5, beyond which the flow rate is observed to decrease. Hence, the magnetic field effect proves to be beneficial only up to a certain magnitude. The flow is noted to augment always with increase in the transverse electric field. It is also observed that after a certain value of the upper plate velocity, the shear force plays the dominant role and there is no enhancement in the flow rate due to the electromagnetic field. The findings may prove significant for design and development of microscale shear flow actuation technologies.