A pressure measurement system for use with a subterranean well can include a chamber positioned in the well, the chamber having an upper portion and a lower portion as positioned in the well, and a device which, in response to gravity acting on the device, selects the upper portion of the chamber for communication with a line extending to a remote location. A method of measuring pressure in a well can include introducing a chamber into the well, then selecting a vertically upper portion of the chamber, and establishing communication between the upper portion of the chamber and a line extending to a remote location.