The interfacial tension between polystyrene (PS) and polybutadiene (PB) homopolymers is measured in the presence of a nearly symmetric poly(styrene-b-butadiene) (SB) copolymer and compared to independent measurements of the critical micelle concentration (CMC) by transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS), and to self-consistent field theory (SCFT) predictions. Interfacial tension is measured with a spinning drop tensiometer (SDT) containing a drop of PB in a PS matrix, using samples in which varying concentrations of SB copolymer were initially added to either PS or PB. When SB is premixed with PS, the dependence of the interfacial tension gamma upon copolymer concentration c is qualitatively similar to that expected in equilibrium, showing a decrease of gamma with increasing c for c less than an apparent CMC and then saturating at higher concentrations. TEM and SAXS studies of a binary mixture of the same copolymer and PS homopolymer show, however, that the true CMC in PS is much lower than the apparent CMC inferred from these SDT experiments. We analyze the role of transport limitations in this experiment and propose that this discrepancy may be a result of a suppressed copolymer chemical potential near the interface due to continual diffusion of copolymer into the PB drop.