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In this Letter, we develop a numerically efficient framework for evaluating parameters in metric theories of gravity, and apply it to constrain the horizon-scale magnetic field in the Kerr-Bertotti-Robinson spacetime using the latest Event Horizon Telescope observations. The method's adaptive ray-tracing strategy achieves near-linear computational efficiency without loss of numerical accuracy. This efficiency allows for high-precision black hole shadow modeling at a minimal computational cost and, for the first time, supports statistically robust parameter inference for arbitrary stationary black holes from horizon-scale observations. Applying the framework to the exact magnetized and rotating Kerr-Bertotti-Robinson solution [Phys. Rev. Lett. 135, 181401 (2025)PRLTAO0031-900710.1103/rfgv-ybz5], we evaluate the horizon-scale magnetic fields of M87* and Sgr A*. The analysis yields a field strength of <inline-formula><mml:math><mml:msubsup><mml:mn>93.3</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>23.8</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>14.7</mml:mn></mml:mrow></mml:msubsup><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>G</mml:mi></mml:math></inline-formula> for Sgr A*, consistent with the 71 G equipartition estimate from polarized Atacama Large Millimeter/submillimeter Array observations, thereby supporting the predictions of Einstein's gravity.