We consider the efficiency limit of relativistic high-order-harmonic emission from solid targets achievable with tailored light fields. Using one-dimensional particle-in-cell simulations, the maximum energy conversion efficiency is shown to reach as high as 10% for the harmonics in the range of 80-200 eV and is largely independent of laser intensity and plasma density. The waveforms most effective at driving harmonics have a broad spectrum with a lower-frequency limit set by the width of the incident pulse envelope and an upper limit set by the relativistic plasma frequency.