We address the problem of fast and accurate computational analysis of large networks of coupled oscillators arising in nanotechnological and biochemical systems. Such systems are computationally and analytically challenging because of their very large sizes and the complex nonlinear dynamics they exhibit. We develop and apply a nonlinear oscillator macromodel that generalizes the well-known Kuramoto model for interacting oscillators, and demonstrate that using our macromodel provides important qualitative and quantitive advantages, especially for predicting self-organization phenomena such as spontaneous pattern formation. Our approach extends and applies recently-developed computational methods for macromodel ling electrical oscillators, and features both phase and amplitude components that are extracted automatically (using numerical algorithms) from more complex differential-equation oscillator models available in the literature. We apply our approach to networks of tunneling phase logic (TPL) and Brusselator biochemical oscillators, predicting a variety of spontaneous pattern generation phenomena. Comparing our results with published measurements of spiral, circular and other pattern formation, we show that we can predict these phenomena correctly, and also demonstrate that prior models (like Kuramoto's) cannot do so. Our approach is more than 3 orders of magnitude faster than techniques that are comparable in accuracy.