This study addresses the challenge of designing functionally graded porous tapered beams (FGPTB) whose natural frequencies are highly sensitive to grading, porosity topology, geometry and boundary conditions. Most existing vibration studies on surrogates optimize only in-distribution accuracy and neglect calibrated reliability under deployment shifts. A machine learning surrogate is needed to deliver accurate, uncertainty-aware predictions of non-dimensional natural frequency (Ω) and to support risk-aware inverse design when boundary conditions, porosity patterns, slenderness, or taper/width ratios differ from the training archive. A higher-order shear deformation theory (HSDT) is used to compute Ω over a Cartesian lattice spanning bi-directional gradient indices (0-10), porosity levels up to 0.3 (even/uneven patterns), aspect ratios 10 and 40, taper and width ratios 0-1.0, and SS/CC supports, yielding 11,616 simulations. Gradient-boosted trees form the backbone regressor, complemented by quantile heads. Split-conformal prediction provides finite-sample valid intervals in-distribution, while importance-weighted conformal recalibrates residual quantiles under covariate shift. Explainability is delivered via uncertainty-aware permutation importance, 1D/2D partial dependence and isotonic overlays. A bi-objective inverse design screen ranks feasible FGPTB configurations on the Pareto plane of absolute error versus calibrated 90% interval width to select knee solutions under manufacturability constraints. Under 5-fold cross-validation, the surrogate attains MAE=0.56, RMSE=0.91 and R²=0.9996. Split-conformal intervals under cover in cross-boundary and regime holdout tests, whereas importance-weighted conformal restores coverage to 0.90 with modest width inflation. Boundary condition and grading dominate Ω, porosity monotonically lowers Ω, and taper/width increases Ω with diminishing returns. Low-frequency targets are met with tight intervals, mid-frequency targets require relaxing porosity/geometry or supports, and high targets trigger calibrated interval inflation, signalling capacity limits. The workflow converts calibrated uncertainty into actionable vibration design decisions for FGPTB and can be extended to higher modes and coupled responses.