The interfacial tension γ between polyisoprene (PI) and polydimethylsiloxane (PDMS) homopolymers mixed with poly(isoprene-b- dimethylsiloxane) (IDMS) diblock copolymers has been measured with a spinning drop tensiometer. Measurements have been conducted for mixtures containing each of 12 copolymers, in which the PDMS volume fraction fDMS varies from 0.49 to 0.73, and for mixtures containing a symmetric copolymer and PI homopolymers of varying molecular weight. The measured interfacial tension is found to be independent of copolymer concentration above an apparent critical concentration of order 0.1 wt % copolymer. Mixtures with a nearly symmetric copolymer are found to exhibit ultralow interfacial tensions, up to 3 orders of magnitude less than that of the bare PI/PDMS interface. Results are compared to the predictions of a numerical self-consistent field theory for the interfacial tension of an interface between a PDMS phase containing swollen spherical micelles and a phase of nearly pure PI. Agreement between theory and experiment is excellent for sufficiently asymmetric copolymers, with fDMS > 0.63. Measured values of γ are significantly lower than predictions for 0.5 < fDMS < 0.6, however, and depend very sensitively upon fDMs over a narrow range 0.60 ≤ fDMS ≤ 0.63. Kinetic limitations that may be relevant to these experiments are also analyzed and discussed.