t-SNE Python implementation: Kullback-Leibler divergence
The TSNE source in scikit-learn is in pure Python. Fit fit_transform() method is actually calling a private _fit() function which then calls a private _tsne() function. That _tsne() function has a local variable error which is printed out at the end of the fit. Seems like you could pretty easily change one or two lines of source code to have that value returned to fit_transform().