Broadly neutralizing Abs against HIV protect from infection, but their routine elicitation by vaccination has not been achieved. To generate small animal models to test vaccine candidates, we have generated targeted transgenic ("knock-in") mice expressing, in the physiological Ig H and L chain loci, two well-studied broadly neutralizing Abs: 4E10, which interacts with the membrane proximal external region of gp41, and b12, which binds to the CD4 binding site on gp120. 4E10HL mice are described in the companion article (Doyle-Cooper et al., J. Immunol. 191: 3186-3191). In this article, we describe b12 mice. B cells in b12HL mice, in contrast to the case in 4E10 mice, were abundant and essentially monoclonal, retaining the b12 specificity. In cell culture, b12HL B cells responded avidly to HIV envelope gp140 trimers and to BCR ligands. Upon transfer to wild-type recipients, b12HL B cells responded robustly to vaccination with gp140 trimers. Vaccinated b12H mice, although generating abundant precursors and Abs with affinity for Env, were unable to rapidly generate neutralizing Abs, highlighting the importance of developing Ag forms that better focus responses to neutralizing epitopes. The b12HL and b12H mice should be useful in optimizing HIV vaccine candidates to elicit a neutralizing response while avoiding nonprotective specificities.