This paper proposes a numerical method for accurate time-domain noise simulation of mixed analogue/digital electrical circuits that in principle do not admit a periodic steady-state working condition, such as fractional sigma phase-locked loops (PLLs). By means of a tool known as saltation matrix, which allows dealing with non-smooth vector fields, a variational approach is adopted. The power spectral density of a noisy electrical variable is computed by applying the Thomson's multitaper method (MTM) to the numerical solution of the stochastic variational model of the circuit. This allows to resort to a single transient simulation run, thus avoiding cpu time consuming Monte-Carlo-like approaches. The effectiveness of the proposed method is shown by comparing simulation results related to a commercial fractional sigma PLL with experimental data.