We present a detailed analysis of binary black hole evolutions in the last orbit and demonstrate consistent and convergent results for the trajectories of the individual bodies. The gauge choice can significantly affect the overall accuracy of the evolution. It is possible to reconcile certain gauge- dependent discrepancies by examining the convergence limit. We illustrate these results using an initial data set recently evolved by Brugmann et al. (Phys. Rev. Lett. 92, 211101 (2004)). For our highest resolution and most accurate gauge, we estimate the duration of this data set's last orbit to be approximately 59MADM. Introduction.—Over the course of the next decade, in- struments capable of detecting gravitational radiation (such as LIGO, VIRGO, TAMA, GEO600) are expected to open a new observational window on the Universe. The collision of binary compact objects such as black holes (BHs) is one of the most promising sources for first gen- eration gravitational wave observatories. The theoretical framework for modeling binary BH (BBH) systems is the complete set of nonlinear Einstein equations. Intensive ef- forts to develop numerical codes able to solve these equa- tions using supercomputers have shown that it is now pos- sible to evolve BHs for periods of an orbit (1-3). If these simulations are to produce waveforms useful for detector searches, high demands are placed on their accuracy (4). The near-zone dynamics of binary BH systems are notoriously difficult to simulate and to analyze. Using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formula- tion and a particular set of gauges, a series of BBH con- figurations, corresponding to initial data in quasicircular orbit at successively larger separations (5), were all found to coalesce in slightly more than a half orbit (2). A similar BSSN evolution carried out using somewhat different gauges and numerical methods for another data set, slightly further out along the orbital sequence, was found to evolve for much more than the estimated orbital time scale 114MADM without finding a common apparent horizon (AH) (1). In fact, no common horizon was found long after the BHs would reasonably be expected to have merged. In this Letter, we carry out an evolution of the same data set and show that it does, indeed, carry out a complete orbit before a common AH forms. As the BH separation de- creases, a local measure of the angular velocityin- creases, so that the duration of the final orbit is approximately 59M. The trajectories are convergent for a range of resolutions and within a class of gauge conditions. However, we do find that very high resolutions are required in order to obtain evolutions close to the contin- uum limit. The resolutions we have applied here are sig- nificantly higher than those used in analogous BH evolutions to date, except for Ref. (3), where similar res- olutions were used. With insufficient resolution, we show that it is possible to substantially under- or overpredict the orbital period. We also find that apparently small devia- tions in the chosen coordinate conditions (gauge), based on the choice of parameters within a particular family, can