A crimp fitting has a monolithic and homogeneous female socket configured to receive and be crimped to an end portion of a tube. The socket comprises an annular wall and an axial opening. The annular wall comprises at least one internal shoulder that protrudes radially inward from the annular wall. A seal ring in the female socket has a C-shaped cross section and is configured to be arranged around the end portion of the tube to be joined with the fitting. The C-shaped seal ring compresses against the internal shoulder after the fitting is crimped with the tube with the C-shaped seal ring arranged around the end of the tube.