A model is discussed for magnetoelectric (ME) effects in a single-crystal ferrite–piezoelectric bilayer on a substrate. The specific focus is on coupling at magneto-acoustic resonance (MAR) at the coincidence of ferromagnetic resonance in the ferrite and thickness modes of the electromechanical resonance in the piezoelectric. The clamping effect of the substrate has been considered in determining the ME voltage coefficient and applied to a model system of a bilayer of lead zirconate titanate (PZT) and yttrium iron garnet (YIG) on a gadolinium gallium garnet substrate. The theory predicts a giant ME effect at MAR due to interaction and transfer of energy between elastic modes and the uniform precession spin-wave mode. It is shown that the ME coupling strength decreases with increasing substrate thickness. Estimates for YIG–PZT for nominal film parameters predict MAR at 5 GHz and ME coefficients on the order of 5–70 V cm⁻¹ Oe⁻¹. The phenomenon is of importance for the realization of multifunctional ME sensors and transducers operating at microwave frequencies.