<p>This paper presents a reduced-order framework for computing bifurcations in a Rayleigh-Bénard problem using a Legendre collocation spectral method as high-fidelity discretization. The framework combines a certified reduced basis method specialized in approximating isolated solution branches, with a reduced-order procedure designed to calculate bifurcation points. The certified method produces, for each branch of solutions, a reduced-order model formulated as a least-squares problem that minimizes the restriction of the high-fidelity residual to a reduced basis. To ensure certification, the reduced bases are built iteratively through a POD-greedy algorithm guided by rigorous a posteriori error estimates. These estimates are defined as the quotient between the high-fidelity residual and a stability factor, which, notably, is approximated using a second reduced basis approach. The reduced-order procedure designed to approximate the bifurcation points accomplishes its purpose by performing an efficient analysis of the regularity of the high-fidelity Jacobian. Numerical results demonstrate that the proposed framework enables accurate, efficient, and reliable computation of the target bifurcation diagram without assuming any a priori knowledge of the bifurcation phenomenon.</p>