This paper presents a scheme to enhance payload manipulation using a robot collaborating with an overhead crane. In the current industrial practice, when the crane's payload has to be accurately manipulated and located in a desired position, the task becomes laborious and risky since the operators have to guide the fine motions of the payload by hand. In the proposed collaborative scheme, the crane lifts the payload while the robot's end-effector guides it toward the desired position. The only link between the robot and the crane is the interaction force produced during the guiding of the payload. Two admittance transfer functions are considered to accomplish harmless and smooth contact with the payload. The first is used in a position-based admittance control integrated with the robot. The second one adds compliance to the crane by processing the interaction force through the admittance transfer function to generate a crane's velocity command that makes the crane follow the payload. Then the robot's end-effector and the crane move collaboratively to guide the payload to the desired location. A method is presented to design the admittance controllers that accomplish a fluent robot-crane collaboration. Simulations and experiments validating the scheme potential are shown.