Several ecological factors that could play into species extinction are expected to correlate with species age, i.e., time elapsed since the species arose by speciation. To date, however, statistical tools to incorporate species age into likelihood-based phylogenetic inference have been lacking. We present here a computational framework to quantify age-dependent extinction through maximum likelihood parameter estimation based on phylogenetic trees, assuming species lifetimes are gamma distributed. Testing on simulated trees shows that neglecting age dependence can lead to biased estimates of key macroevolutionary parameters. We then apply this method to two real data sets, namely a complete phylogeny of birds (class Aves) and a clade of self-compatible and -incompatible nightshades (Solanaceae), gaining initial insights into the extent to which age-dependent extinction may help explain macroevolutionary patterns. Our methods have been added to the R package TreePar.