Spectral analysis is applied to tremor time series in basic research and treatment monitoring. The estimation of the spectra from the data is usually done by averaging the squared modulus of the Fourier transform of segments of the data. We discuss drawbacks of this method and propose an alternative procedure to estimate the spectra adaptively based on the data. Thus, the method can be applied to all types of tremor. Applying the theory of spectral estimation, we propose a method to decide whether a spectrum exhibits multiple significant peaks and discuss different approaches to determine the amplitude of the tremor from the spectrum.