It is known that the Lipschitz-free space $\mathcal{F}(M)$ over a proper metric space $M$ is a dual Banach space if and only if $M$ is purely $1$-unrectifiable. In this case, a natural predual is given by the space of (uniformly) locally flat Lipschitz functions that are flat at infinity. Beyond the proper setting, however, much less is understood. In this talk, we give a metric characterisation of when the Lipschitz-free space over a separable ultrametric space is a dual space and show how this result improves upon previous knowledge, including an example of a bounded uniformly discrete ultrametric space whose Lipschitz-free space is not a dual.