score or cost function for AgglomerativeClustering
Don't run agglomerative clustering with multiple n_clusters, that is just unnecessary.

Agglomerative clustering is a two-step process (but the sklearn API is suboptimal here, consider using scipy itself instead!).


Construct a dendrogram
Decide where to cut the dendrogram


The first step is expensive, so you should only do this once. It does not yet produce clusters, but the Dendrogram which can be helpful to decide on the number of clusters. In the -cheap- second step, clusters are then extracted. You can use the height value of the dendrogram in a similar way as inertia with k-means. In fact, the height with Ward linkage is very closely related to inertia. But the same drawbacks apply: the value is (for most linkages) monotone. So it's not too helpful for choosing upon the number of clusters naively.