Power systems with a large share of inverter-based resources lack the inertial response found in systems with traditional synchronous generation. Lower inertia makes power systems vulnerable to undesirable large frequency and rate of change of frequency (RoCoF) deviations, which can lead to system break up. Energy storage systems can be utilized to provide fast-frequency support to prevent such large frequency excursions. However, there are several challenges to implementing effective fast-frequency support. Real-time power system situational awareness (measurements and communication) is required along with real-time estimates of the system’s frequency and RoCoF. Measurement noise, as is common in phase-locked loop measurements, and time delays, which are common when using low-pass filters as in traditional derivative-based (virtual inertia) controllers, can have significant negative impacts on system stability and the performance of frequency support. System parameters such as inertia and damping constants can change in real-time operation and must be accommodated in the system’s fast-frequency response. Moreover, fast-frequency support is a power-intensive application that can significantly impact the lifetime of energy storage systems. This chapter describes an optimization-based framework for estimating frequency, RoCoF, and system parameters, along with leveraging energy storage systems to provide power injections for fast-frequency support service for low inertia microgrids. The framework directly addresses the challenges previously described. Specifically, the framework maintains a desired quality-of-service (limiting the frequency and RoCoF excursions) while explicitly considering the energy storage system lifetime and physical limits. The framework utilizes Moving Horizon Estimation to estimate system frequency and RoCoF from noisy Phase-Locked Loop measurements, as well as system parameters such as microgrid inertia and damping constants. These estimates are then employed by a Model Predictive Control algorithm that computes energy storage power injections to provide fast frequency support. This optimization-based approach provides effective estimates and avoids undesired oscillations that degrade system performance. The framework’s effectiveness is demonstrated in simulations of a benchmark low inertia microgrid.