A method of pressure testing a well tool can include applying positive or negative pressure to an internal chamber of the well tool, or determining a reference pressure, and monitoring the pressure in the internal chamber using a pressure sensor in the internal chamber. Another method can include applying pressure to an internal chamber of a well tool at a surface location, thereby creating a pressure differential in one direction across a seal, and installing the well tool in a well, thereby creating another pressure differential in a possibly opposite direction across the seal. A well system can include a well tool including an internal chamber, and a pressure sensor disposed in the chamber, whereby the pressure sensor detects pressure within the chamber.