Active electrosense is used by some fish for the sensing of nearby objects by means of the perturbations the objects induce in a self-generated electric field. As with echolocation (sensing via perturbations of an emitted acoustic field) active electrosense is particularly useful in environments where darkness, clutter or turbidity makes vision ineffective. Work on engineered variants of active electrosense is motivated by the need for sensors in underwater systems that function well at short range and where vision-based approaches can be problematic, as well as to aid in understanding the computational principles of biological active electrosense. Prior work in robotic active electrosense has focused on tracking and localization of spherical objects. In this study, we present an algorithm for estimating the size, shape, orientation, and location of ellipsoidal objects, along with experimental results. The algorithm is implemented in a robotic active electrosense system whose basic approach is similar to biological active electrosense systems, including the use of movement as part of sensing. At a range up to '20 cm, or about half the length of the robot, the algorithm localizes spheroids that are one-tenth the length of the robot with accuracy of better than 1 cm for position and 5°in orientation. The algorithm estimates object size and length-to-width ratio with an accuracy of around 10%.