We present a combined numerical and asymptotic approach for modeling droplets in microchannels. The magnitude of viscous forces relative to the surface tension force is characterized by a capillary number, Ca, which is assumed to be small. The numerical results successfully capture existing asymptotic solutions for the motion of drops in unconfined and confined flows; examples include the analytic Stokes flow solution for a two-dimensional inviscid bubble placed in an unbounded parabolic flow field and asymptotic formulas for slender bubbles and drops in confined flows. An extensive investigation of the accuracy of the computations is presented to probe the efficacy of the methodology and algorithms. Thereafter, numerical simulations are presented for droplet breakup in a symmetric microfluidic T-junction. The results are shown to support a proposed mechanism for breakup, driven by a pressure drop in a narrow gap between the droplet and the outer channel wall, which was formally derived in the limit Ca(1/5) << 1 [A. M. Leshansky and L. M. Pismen, "Breakup of drops in a microfluidic T junction," Phys. Fluids 21, 023303 (2009)]. (C) 2011 American Institute of Physics.