Background: Phase-amplitude coupling (PAC) - the dependence of the amplitude of one rhythm on the phase of another, lower-frequency rhythm - has recently been used to illuminate cross-frequency coordination in neurophysiological activity. An essential step in measuring PAC is decomposing data to obtain rhythmic components of interest. Current methods of PAC assessment employ narrowband Fourier-based filters, which assume that biological rhythms are stationary, harmonic oscillations. However, biological signals frequently contain irregular and nonstationary features, which may contaminate rhythms of interest and complicate comodulogram interpretation, especially when frequency resolution is limited by short data segments. New method: To better account for nonstationarities while maintaining sharp frequency resolution in PAC measurement, even for short data segments, we introduce a new method of PAC assessment which utilizes adaptive and more generally broadband decomposition techniques - such as the empirical mode decomposition (EMD). To obtain high frequency resolution PAC measurements, our method distributes the PAC associated with pairs of broadband oscillations over frequency space according to the time-local frequencies of these oscillations. Comparison with existing methods: We compare our novel adaptive approach to a narrowband comodulogram approach on a variety of simulated signals of short duration, studying systematically how different types of nonstationarities affect these methods, as well as on EEG data. Conclusions: Our results show: (1) narrowband filtering can lead to poor PAC frequency resolution, and inaccuracy and false negatives in PAC assessment; (2) our adaptive approach attains better PAC frequency resolution and is more resistant to nonstationarities and artifacts than traditional comodulograms.