Fast estimation methods for small outage probabilities of signaling in fading multiple-input multiple-output (MIMO) channels are developed. Communication over such channels is of much current interest, and quick and accurate methods for estimating outage capacities are needed. The methods described herein use adaptive importance sampling (IS) techniques as developed in a series of recent publications. Fast algorithms are provided for evaluating "nonergodic" capacities of Rayleigh fading MIMO channels. The methodology can be extended to more general models. Numerical results on outage capacity are provided, and these extend and complement known results in the literature.