We show how branch ambiguities in the extraction of effective parameters is arising as a direct consequence of the underlying Bloch state physics. The mutual importance of the different branches in general depends on the experimental context, and we show how the Fourier spectrum of the field inside the metamaterial can be used to access this. Different numerical examples illustrate how a predominant branch may be identified for l a while at higher frequency the power may be distributed over more branches. This is in particular true near bandedges and strong resonances. Extensions to two- and three-dimensional metamaterial designs are discussed.