Buckling-restrained braces (BRBs) are capable of withstanding severe seismic demands without visible damage or requiring replacement. However, stability must be maintained to achieve this performance. While the restrainer design is well established, current guidance to ensure connection stability differs markedly from country to country and the recommended methods produce a wide range of predicted capacities. This is an issue that has been discussed in the commentary to AISC 341 since the 2005 edition, but the specific method of analysis is currently left to the engineer's judgement. This paper evaluates the accuracy of the stability evaluation methods currently being used by engineers in Japan, New Zealand, Taiwan and the US, based on a test catalogue of 82 specimens, 50% of which experienced out-of-plane connection buckling. This is a global mode characterized by the formation of a hinge just outside of the restrainer, with the gusset subsequently yielding to complete the collapse mechanism. Several recently proposed methods are shown to be conservative, and the critical design variable is identified as the out-of-plane rotational end fixity provided by the gusset and adjacent framing. A three-tier design procedure is proposed, with each tier producing a less conservative design, but at the cost of increased analytical effort.