Detailed spectroscopic and imaging observations of colliding elliptical galaxies have revealed unmistakable diagnostic signatures of the tidal interactions. It is possible to compare both the distorted luminosity distributions and the disturbed internal rotation profiles with numerical simulations in order to model the strength of the tidal gravitational field acting within a given pair of galaxies. Using the best-fit numerical model, one can then measure directly the mass of a specific interacting binary system. This technique applies to individual pairs and therefore complements the classical methods of measuring the masses of galaxy pairs in well-defined statistical samples. The “personalized” modeling of galaxy pairs also permits the derivation of each binary’s orbit, spatial orientation, and interaction timescale. Similarly, one can probe the tides in less-detailed observations of disturbed galaxies in order to estimate some of the physical parameters for larger samples of interacting galaxy pairs. These parameters are useful inputs to the more universal problems of (1) the galaxy merger rate, (2) the strength and duration of the driving forces behind tidally-stimulated phenomena (e.g., starbursts and maybe QSOs), and (3) the identification of long-lived signatures of interaction/merger events.