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Recently, locally resonant metamaterials have come to the fore in noise and vibration control engineering, showing great potential due to their superior noise and vibration attenuation performance in targeted and tunable frequency ranges, referred to as stop bands. Damping has an important influence on the performance of these materials, broadening the frequency range of attenuation at the expense of peak attenuation. As a result, understanding and including the effects of damping is necessary to more accurately predict the attenuation performance of these locally resonant metamaterials. Classically, these often periodic structures are analysed using a unit cell modelling approach to predict wave propagation and thus stop band behaviour, discarding damping. In this work, a unit cell method including damping is used to analyse the complex dispersion curves of a locally resonant metamaterial design. The wave solutions in and around the stop band frequency range are compared to those of the unit cell method discarding damping. The influence on the dispersion curves of damping in resonator and host structure is discussed and the obtained dispersion curves are validated through an experimental dispersion curve measurement based on an Extended Inhomogeneous Wave Correlation method using Scanning Laser Doppler Vibrometry for a metamaterial plate manufactured at a representative scale. Excellent agreement is obtained between the numerically predicted and experimentally retrieved dispersion curves.