Push-buttons provide rich haptic feedback during a press via mechanical structures. While different buttons have varying haptic qualities, few works have attempted to dynamically render such tactility, which limits designers from freely exploring buttons' haptic design. We extend the typical force-displacement (FD) model with vibration (V) and velocity-dependence characteristics (V) to form a novel FDVV model. We then introduce Press'Em, a 3D-printed prototype capable of simulating button tactility based on FDVV models. To drive Press'Em, an end-to-end simulation pipeline is presented that covers (1) capturing any physical buttons, (2) controlling the actuation signals, and (3) simulating the tactility. Our system can go beyond replicating existing buttons to enable designers to emulate and test non-existent ones with desired haptic properties. Press'Em aims to be a tool for future research to better understand and iterate over button designs.