Buckling-restrained braces (BRBs) achieve large peak and cumulative ductility capacities by restricting yielding to an encased core, while maintaining global stability. However, stability is often governed by the connections and is sensitive to the end fixity provided by the adjacent framing and gusset, and flexural continuity between the neck and restrainer. This paper presents simple analytical methods to determine the flexural properties of these key components. Full-depth gusset stiffeners are found to be highly effective in increasing the out-of-plane rotational stiffness (KRg), equivalent to doubling the thickness. An equivalent connection is proposed to account for the adjacent framing (KRf), but this may be neglected if KRf > 10∙KRg. This is typically satisfied if a diaphragm slab and transverse beam are provided, but may exceed beam torsional bracing requirements. The restrainer end moment transfer capacity is extended to mortar-filled RHS restrainers, confirming that neck insert ratios of Lin/Bn > 2.0 are required for full continuity.