We fit binary lens models to the data covering the initial part of real mic
rolensing events in an attempt to predict the time of the second caustic cr
ossing. We use approximations during the initial search through the paramet
er space for light curves that roughly match the observed ones. Exact metho
ds for calculating the lens magnification of an extended source are used wh
en we refine our best initial models. Our calculations show that the reliab
le prediction of the second crossing can only be made very late, when the l
ight curve has risen appreciably after the minimum between the two caustic
crossings. The best observational strategy is therefore to sample as freque
ntly as possible once the light curve starts to rise after the minimum.