Circuit optimization is an indispensable step in analog/RF IC design. Classical fast gradient-based optimization methods are typically infeasible due to lack of access to simulator source code and the technical barriers to implementing adjoint methods. Therefore, surrogate-based black-box optimization is widely used in practice; however, it can be costly to build and sensitive to hyperparameters, whereas population heuristics often suffer from slow convergence and large evaluation counts under tight simulator-call budgets. To address these limitations, we propose the Zeroth-Order Analog/RF Framework (ZOAF), which recovers gradient-descent directions from a small number of black-box circuit simulations, combining the benefits of both gradient-based optimization and black-box optimization. We also employ several surrogate-free techniques to improve the efficiency and accuracy, including (1) a hybrid ZO scheduling method that switches between random-direction ZO for budget-efficient exploration and coordinate-wise ZO for accurate late-stage refinement, (2) one-shot quasi-random multi-start to focus evaluations, and (3) a sliding-window monitor that triggers early stops and box-projected updates to maintain feasibility. Evaluated on three distinct schematics, ZOAF consistently outperforms state-of-the-art baselines, achieving the best median final value on every reported figure of merit -- with up to an order-of-magnitude advantage in median peaking on the 22-parameter two-stage amplifier -- together with the most robust worst-case behavior across seeds, while reducing simulator calls to convergence by $1.3$--$3.8\times$. Code is publicly available at https://github.com/LiyanTan111/ZOAF.

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