A support and connection system for a riser run from a subsea well to a floating vessel has a female housing supported from the vessel that receives a male termination head secured to the riser string. The termination head fits within a tapered bore in the termination housing. Radial ports connect with radial passages in the termination head for transmitting fluids to and from the vessel and subsea well. A compound curved seat prevents jamming of the termination housing in the termination head due to the high tension placed on the termination housing. The seat is annular and also curves in a vertical direction.