Gravitational waves from coalescing binary black holes encode the evolution of their spins prior to merger. In the post-Newtonian regime and on the precession time scale, this evolution has one of three morphologies, with the spins either librating around one of two fixed points ("resonances") or circulating freely. In this paper we perform full parameter estimation on resonant binaries with fixed masses and spin magnitudes, changing three parameters: a conserved "projected effective spin" ξ and resonant family ΔΦ=0,π (which uniquely label the source); the inclination θJN of the binary's total angular momentum with respect to the line of sight (which determines the strength of precessional effects in the waveform); and the signal amplitude. We demonstrate that resonances can be distinguished for a wide range of binaries, except for highly symmetric configurations where precessional effects are suppressed. Motivated by new insight into double-spin evolution, we introduce new variables to characterize precessing black hole binaries which naturally reflects the time scale separation of the system and therefore better encode the dynamical information carried by gravitational waves.