We have developed an app, named Sunpass, that is able to convert every smartphone into a solar compass. Sunpass uses input data from the smartphone sensors, calculates the Sun position, and elaborates data to give the desired information. The azimuth values measured by a smartphone equipped with Sunpass show a typical accuracy of 0.5°, which is limited by camera aberrations and misalignment of both accelerometer and CCD camera of the smartphone. In this paper, we show that both accuracy and reliability in azimuth measurements can be improved by a specific calibration procedure and a dedicated mechanical tool. We obtained a remarkable accuracy better than 0.06° on the single azimuth measurements, which improves to 0.03° on the average of eight measurements.