Self-assembled wormlike micelles (WLMs) are of particular scientific and technological interest due to their ability to branch, break, and reform under shear, which can lead to nonlinear flow phenomena and instabilities such as shear banding [1,2]. As measuring chain branching in polymer physics is a long-standing scientific challenge, branched WLMs are also used as a model system for studying branched polymers. Nonlinear rheology and large amplitude oscillatory shear (Laos) have shown to be useful in the study of chain branching , but quantitative relationships are still lacking. Thus, understanding the coupling between flow behavior and molecular topology requires experimental methods that combine time- and spatially-resolved small angle neutron scattering (SANS) measurements of structure with rheometry for nonlinear deformations . Here, we explore the relationship between branching, microstructure and nonlinear responses using a series of well-characterized, branched WLM solutions [1, 5-7]. While micellar branching is physically distinct from chemical branching in polymers , we observe similar responses under shear startup and Laos [3, 9].