This paper presents high-resolution control of torsional electrostatic micromirrors beyond their inherent pull-in instability using robust sliding-mode control (SMC). The objectives of this paper are two-fold - firstly, to demonstrate the applicability of SMC for MEMS devices; secondly - to present a modified SMC algorithm that yields improved control accuracy. SMC enables compact realization of a robust controller tolerant of device characteristic variations and nonlinearities. Robustness of the control loop is demonstrated through extensive simulations and measurements on MEMS with a wide range in their characteristics. Control of two-axis gimbaled micromirrors beyond their pull-in instability with overall 10-bit pointing accuracy is confirmed experimentally. In addition, this paper presents an analysis of the sources of errors in discrete-time implementation of the control algorithm. To minimize these errors, we present an adaptive version of the SMC algorithm that yields substantial performance improvement without considerably increasing implementation complexity.