A layer of Rivlin-Ericksen viscoelastic fluid heated from below is considered in the presence of uniform vertical magnetic field. Following the linearized stability theory and normal mode analysis, the paper through mathematical analysis of the governing equations of Rivlin-Ericksen viscoelastic fluid convection with a uniform vertical magnetic field, for any combination of perfectly conducting free and rigid boundaries of infinite horizontal extension at the top and bottom of the fluid, established that the complex growth rate ? of oscillatory perturbations, neutral or unstable for all wave numbers, must lie inside a semi-circle in the right half of a complex r i ? ? -plane, where Q is the Chandrasekhar number and F is the viscoelastic parameter of the Rivlin-Ericksen fluid, which prescribes the upper limits to the complex growth rate of arbitrary oscillatory motions of growing amplitude in the couple-stress fluid heated from below in the presence of uniform vertical magnetic field. The result is important since the result hold for all wave numbers and the exact solutions of the problem investigated in closed form, are not obtainable for any arbitrary combinations of perfectly conducting dynamically free and rigid boundaries.