The Central American Seaway played a pivotal role in shaping global climate throughout the late Cenozoic. Recent geological surveys have provided new constraints on timing of the seaway shoaling, while neodymium isotopic (εNd) data measured on fossil teeth, debris, and ferromanganese crusts have helped define the history of water masses in the region. Here we provide the first 3‐D simulations of εNd responses to the shoaling seaway. Our model suggests that a narrow and shallow seaway is sufficient to affect interoceanic circulation, that inflow/outflow balance between the Caribbean and the Antilles responds nonlinearly to sill depth, and that a seaway narrower than 400 km is consistent with an active Atlantic meridional overturning circulation during the late Miocene. Simulated εNd values in the Caribbean confirm that inputs from radiogenic Pacific waters in the Caribbean decrease as the seaway shoals. Despite model limitations, a comparison between our results and εNd values recorded in the Caribbean helps constrain the depth of the Central American Seaway through time, and we infer that a depth between 50 and 200 m could have been reached 10 Ma ago. Key Points Model/data comparison of epsilon Nd suggests a shallow CAS during the Miocene CAS throughflow depends on seaway geometry and atmospheric coupling Ocean circulation responds nonlinearly to CAS shoaling