This work describes and compares two phase-locked-loop (PLL) algorithms aimed at tracking a biased sinusoidal signal with unknown frequency, amplitude, and phase, with inherent robustness to dc offset. The proposed methods endow quadrature PLLs, renowned for their excellent tracking performance, with frequency-adaptation capability, while providing robust global stability certificates. The large-gain global stability, proved by Lyapunov-like arguments borrowed from adaptive control theory, represents a major benefit when compared to the conventional PLLs, whose convergence instead can be proved only locally by small-signal analysis or small-gain assumptions. In this connection, the proposed algorithms represent the first frequency-adaptive and dc-bias rejecting PLL-type architectures with Lyapunov-certified global stability. When used for signal tracking, the proposed methods are shown to outperform the adaptive observer, especially in noisy conditions. Moreover, they provide more accurate frequency estimates than existent frequency-adaptive PLLs, showing enhanced robustness in facing both phase-noise and measurement perturbations.