A surgical clamp has pivoting jaws with undulating arrays of teeth that are interdigitating and offset with relation to each other. This clamp structure assures a firm, non-slipping grip in the presence of blood and body fluids during surgery. The inner surfaces of the jaws are concave to allow the clamp to grasp more tissue or organ that would be possible with flat inner surfaces. Laparoscopic and open surgery embodiments are included. An alternative to the embodiment is a clamp having openings through which tissue or an organ can protrude to allow an even greater amount of tissue or organ to be grasped.