The sensor orthogonality and azimuth accuracy of a seismometer at a seismic station are generally important parameters for data quality control. These parameters can be estimated using suitable methods with an appropriately defined coordinate system and related angle set. We compare three methods with synthetic data and real data to investigate their validity and consistency. Using synthetic data generated from real records of an instrument system (which is composed of an STS2.5 seismometer connected to an Q330HRS recorder), numerical experiments reveal relationships between estimation errors and statistical noise level, as well as timing error. Because the original method described by Tasič and Runovc (2013) discards some possible solutions, it can lead to an ambiguous azimuth result. This can be avoided by taking into account complete solutions, as well as by constraining the vertical inclination and orthogonal deviation solutions to quadrants I and IV. This can lead to results that are closer to possible physical conditions. Real records at stations BJT, Jiujiang, and Mengcheng are processed, including microseism and earthquake event data. All three methods yield consistent results once the method of Tasič and Runovc (2013) is modified to consider the complete solutions and the constraints of physical conditions. If different data recorders are used for the reference and test seismometers, sample time shifts can affect the estimated vertical axis inclination angle; this can be used to assess timing offset between the two recorders. [ABSTRACT FROM AUTHOR]