The frequency of relaxation oscillations in the output power of lasers, particularly semiconductor lasers, is an important parameter which can be used to inform other fundamental laser variables, for comparison with expected theory, and to show the effect of external influences, such as optical feedback, by a change in value. Thus, precision measurement of the relaxation frequency is important. Instantaneous frequency measurement algorithms are applied to experimental semiconductor laser relaxation-oscillation signals to determine whether reliable values can be extracted, for an extended range of injection current, as compared to direct measurement and fast Fourier transform techniques. Improvement is achieved but, more importantly, the technique clearly shows when other oscillations, such as those due to packaging, connectorization and power supply, dominate the oscillatory component of the output power, at low injection currents. The work further supports the finding that only mid-range injection currents can be used for reliable precision relaxation oscillation frequency measurement.