Cocontinuous morphologies of polymer blends are thermodynamically unstable: they will coarsen when held above their glass or melting transition temperature. We have found that properly chosen diblock copolymers (bcp) can arrest coarsening during quiescent annealing. The effects of bcp on the cocontinuous morphologies of polystyrene (PS)/polyethylene (PE), PS/poly(methyl methacrylate) (PMMA) and PS/styrene-ran-acrylonitrile copolymer (SAN) blends were studied using scanning electron microscopy (SEM) and laser scanning confocal microscopy (LSCM) with image analysis. Bcp effectiveness was dependent on copolymer molecular weight, concentration, and asymmetry. Our interpretation emphasizes the role of bcp micelle creation and destruction as potential bottlenecks in the kinetics of interfacial adsorption of copolymer during mixing and of interfacial desorption during coarsening. In cases where adsorption and desorption appear to be facile, our results for the rate of coarsening are consistent with equilibrium predictions from self-consistent field theory for the dependence of interfacial tension upon copolymer asymmetry. We show that the coarsening of cocontinuous blends can provide a method to quantify the reduction in interfacial tension due to block copolymer addition, which is difficult to measure by conventional methods.