Vibration protection of sensitive electronic equipment which operates in harsh environments often relies on resilient mounts. The traditional optimal design of vibration isolation from harmonic vibration is based on compromising damping and stiffness properties of mounts and is aimed, in general, at widening the frequency range over which the attenuation takes place, subject to limitations imposed on the rattlespace of the electronic box. Such a design typically incurs the use of heavily damped vibration isolators. Nevertheless, the reliability of the electronic instrumentation depends not only on the level of vibration experienced by the electronic box, but also, and primarily, on the vibration responses of the internal components that are often lightly damped and extremely responsive over a wide frequency range. The traditional approach, however, completely ignores the presence of such components. The heavily damped vibration isolators result in poor vibration isolation over the high-frequency span which typically contains resonant frequencies for critical internal components and, therefore, are insufficient for maintaining a fail-safe vibration environment for electronic equipment. The proposed design approach focuses primarily on the dynamic properties and responses of the critical internal components of an electronic device. In this instance, the heavy and rigid electronic box is thought of and utilised as the first-level vibration isolation stage (mechanical low-pass filter) relative to the sensitive internal components. The optimally chosen elastic and damping properties of the vibration isolators minimise the vibration experienced by the critical internal components, subject to restraints imposed on the peak deflections of the electronic box. The optimisation procedure relies on an analytical solution. The results of calculations are proven experimentally.