A semiconductor die includes proximity connectors proximate to a surface of the semiconductor die. This semiconductor die is configured to communicate signals with another semiconductor die via proximity communication through one or more of the proximity connectors. In particular, the proximity connectors include a first group of proximity connectors that is configured to facilitate determining a first separation between the semiconductor die and the other semiconductor die by comparing coupling capacitances between the semiconductor die and the other semiconductor die. Note that the first group of proximity connectors includes a first proximity connector and a second proximity connector, and the second proximity connector at least partially encloses an in-plane outer edge of the first proximity connector.