**Abstract** Phase-field models, particularly the Allen–Cahn (AC) and Cahn–Hilliard (CH) equations, are fundamental for studying interfacial dynamics but pose severe numerical challenges due to their sharp transition layers and stiffness. Although physics-informed neural networks (PINNs) offer a mesh-free alternative, deep networks suffer from non-convex optimization, ill-conditioned gradients, and extensive hyperparameter tuning, often limiting accuracy to moderate error levels (e.g., \(10^{-2}\)) at high training costs. To circumvent these intrinsic difficulties, we develop a comprehensive random projection neural network (RPNN) framework—also known as random feature methods or extreme learning machines—for solving phase-field models. Unlike deep PINNs, RPNNs freeze randomly initialized hidden-layer parameters and reformulate the training task as a deterministic (non)linear least-squares problem, enabling efficient Newton-type solvers. We systematically investigate critical architectural factors governing RPNN performance, including initialization strategies, the random feature range \(R_m\), seven distinct activation functions, and dense versus separable space-time basis constructions. To address the scale disparity and smoothness mismatch inherent in the fourth-order CH equation, we introduce independent random feature bases for the order parameter \(u\) and chemical potential \(\mu\), complemented by a suite of enhancement strategies: residual-based adaptive refinement (RAR), energy-dissipation-rate adaptive sampling (EDRAS), gradient-based adaptive sampling, residual reweighting, and mild derivative-penalty regularization. Extensive numerical experiments demonstrate that our RPNN framework consistently outperforms state-of-the-art deep PINNs by one to two orders of magnitude in both relative mean square error and $L^\infty$ error under matched conditions, achieving accuracy as low as $8.64\times10^{-4}$ relative $L^2$ error and $1.39\times 10^{-3}$ $L^\infty$ error for the CH equation while providing a continuous spatio-temporal representation. These results establish RPNNs as a highly efficient and robust alternative for sharp-interface phase-field simulations.