Ancient DNA (aDNA) is increasingly being used to investigate questions such as the phylogenetic relationships and divergence times of extant and extinct species. If aDNA samples are sufficiently old, expected branch lengths (in units of DNA substitutions) are reduced relative to contemporary samples. This can be accounted for by incorporating sample ages into phylogenetic analyses. Existing methods that use tip (sample) dates infer gene trees rather than species trees, which can lead to incorrect or biased inferences of the species tree. Methods using a multispecies coalescent (MSC) model overcome these issues. We developed an MSC model with tip dates and implemented it in the program bpp. The method performed well for a range of biologically realistic scenarios, estimating calibrated divergence times and mutation rates precisely. Simulations suggest that estimation precision can be best improved by prioritizing sampling of many loci and more ancient samples. Incorrectly treating ancient samples as contemporary in analyzing simulated data, mimicking a common practice of empirical analyses, led to large systematic biases in model parameters, including divergence times. Two genomic datasets of mammoths and elephants were analyzed, demonstrating the method's empirical utility.