The decomposition of gl-representations when restricted to sp is a classic problem in representation theory, commonly referred to as symplectic branching. The multiplicities that describe this decomposition have a known combinatorial description in terms of certain Littlewood-Richardson tableaux. In this work, we construct an explicit and elementary bijection between the sp-highest weight vectors in the gl-crystals and these tableaux. Thus, we are able to present an alternative interpretation for the symplectic branching, visualizing it at the crystal level.