A swivel misalignment coupling for connecting pipe sections in a high-pressure conduit. In one embodiment, the coupling is a three-bolt coupling having a female coupling member, a male coupling member, and a swiveling collar member. The male and female coupling members have contact surfaces that are spherical to enable sealing contact between them. A seal ring may be positioned between the contact surfaces to ensure a good seal. The collar swivels around the male coupling member to facilitate fastening of the collar to the female coupling member, which holds the male and female coupling members in sealing engagement. Recesses may be positioned radially inward from the attachment points (e.g., bolt holes) of the female coupling member to reduce stress and potential deformation of the contact surface.