Electromagnetic metamaterials are artificially constructed media composed of arrays of electrical circuits that can exhibit electric and magnetic characteristics unlike those of any conventional materials. However, the materials are lossy and hence noisy, so that the signal-to-noise ratio in practical situations is greatly reduced. In particular, operating in the double negative region, where both the permittivity and the permeability are negative so that the refractive index is real but negative, incurs significant loss and noise penalties. In this work, we report noise measurements on a double negative metamaterial at microwave frequencies and compare them with the results of a simple model based on a transmission line loaded with lossy elements that mimic the split ring resonators and fine wires of the metamaterial. A noise source is associated with the resistive part of each element, and these are added incoherently to predict the total noise spectrum of the metamaterial. The theoretical results are in good agreement with the measurements. In particular, we find that the measured noise spectrum has contributions from both electric and magnetic noise, but is dominated by the magnetic noise. This limits possible applications, even with optimised materials, to functions that cannot be realised by conventional means.