We propose two-stage methods for selection and multiple comparisons with the best (MCB) of steady-state performance measures of regenerative systems. We assume the systems being compared are simulated independently, and the methods presented are asymptotically valid as the confidence-interval width parameter shrinks and the first-stage run length grows at a rate that is at most the inverse of the square of the confidence-interval width parameter. When the first-stage run length is asymptotically negligible compared to the total run length, our procedures are asymptotically efficient. We provide an asymptotic comparison of our regenerative MCB procedures with those based on standardized time series (STS) methods in terms of mean and variance of total run length. We conclude that regenerative MCB methods are strictly better than STS MCB methods for any fixed number of batches, but the two become equivalent as the number of batches grows large.