Time-delay estimation is studied for cognitive radio systems, which facilitate opportunistic use of spectral resources. A two-step approach is proposed to obtain accurate time-delay estimates of signals that occupy multiple dispersed bands simultaneously, with significantly lower computational complexity than the optimal maximum likelihood (ML) estimator. In the first step of the proposed approach, an ML estimator is used for each band of the signal in order to estimate the unknown parameters of the signal occupying that band. Then, in the second step, the estimates from the first step are combined in various ways in order to obtain the final time-delay estimate. The combining techniques that are used in the second step are called optimal combining, signal-to-noise ratio (SNR) combining, selection combining, and equal combining. It is shown that the performance of the optimal combining technique gets very close to the Cramer-Rao lower bound at high SNRs. These combining techniques provide various mechanisms for diversity combining for time-delay estimation and extend the concept of diversity in communications systems to the time-delay estimation problem in cognitive radio systems. Simulation results are presented to evaluate the performance of the proposed estimators and to verify the theoretical analysis.