Ultrasound localization microscopy (ULM) is a vascular imaging method that provides a 10-fold improvement in resolution compared to ultrasound Doppler imaging. Because typical ULM acquisitions accumulate large numbers of synthetic microbubble (MB) trajectories over hundreds of cardiac cycles, transient hemodynamic variations such as pulsatility get averaged out. Here we introduce two independent processing methods to retrieve pulsatile flow characteristics from MB trajectories sampled at kilohertz frame rates and demonstrate their potential on a simulated dataset. The first approach follows a Lagrangian description of the flow. We filter the MB trajectories to eliminate ULM localization grid artifacts and successfully recover the pulsatility fraction Pf with a root mean square error (RMSE) of 3.3%. Our second approach follows a Eulerian description of the flow. It relies on the accumulation of MB velocity estimates as observed from a stationary observer. We show that pulsatile flow gives rise to a bimodal velocity distribution with peaks indicating the maximum and minimum velocities of the cardiac cycle. In this second method, we recovered the pulsatility fraction Pf by measuring the location of these distribution peaks with a RMSE of 5.2%. We evaluated the impact of the MB localization precision σ on our ability to retrieve the bimodal signature of a pulsatile flow. Together, our results demonstrate that pulsatility can be retrieved from ULM acquisitions at kilohertz frame rate and that the estimation of the pulsatility fraction improves with localization precision.