Telepresence robots act as the remote embodiments of human operators, enabling people to stay connected to friends, family, and coworkers over lengthy physical separations. However, the factors affecting how humans can best make use of such systems are not yet well understood. This paper explores the effects of personalization and relationship closeness on telepresence via two studies. Study 1 was a between-participants experiment that investigated telepresence robot personalization. 32 pairs of friends (N = 64) participated in the study's team-building-style activities and answered questions about robot operator presence. The results unexpectedly indicated that relationship closeness influenced the interaction experience more than any other considered predictor variable. To study closeness more rigorously as the central manipulation, we conducted Study 2, a between-participants experiment with 24 pairs (N = 48) and a similar procedure. Robot operators who reported a closer relationship with their teammate felt more present in this investigation. These findings can inform the design and application of telepresence robot systems to increase a remote operator's feelings of presence via robot.