We measured the anisotropy of Tb3+ and Eu3+ in various chelate complexes bound with or without a carbostyril antenna. The anisotropy of the lanthanides depends on the chelate as well as whether the antenna is present. The anisotropy of Eu3+ bound to only a chelate is high while for Tb3+ the anisotropy is nearly zero. For Eu3+, the anisotropy decreases upon addition of the antenna, while for Tb3+ the anisotropy slightly increases once the antenna is attached. A theoretical model is discussed to account for the measured anisotropy of the Eu3+ bound to the chelate and how the addition of the antenna affects the anisotropy. While the transitions within Tb3+ are more complicated than those in Eu3+, the theoretical model is also extended to, Tb3+ to explain qualitatively how the addition of the antenna affects the measured anisotropy of the terbium complex. Because of their low anisotropy, both Tb3+ and Eu3+, when bound to a chelate with an antenna, are ideal luminescent probes in resonance energy transfer experiments for measuring nanometer scale distances. Our results indicate that it may be possible to construct a probe with Eu3+ that retains its high anisotropy once the antenna is added to the chelate complex. This probe could measure rotational motion on the millisecond lifetime.