The energy consumption of worm robots is composed of three parts: heat losses in the motors, internal friction losses of the worm device and mechanical energy locomotion requirements which we refer to as the cost of transport (COT). The COT, which is the main focus of this paper, is composed of work against two types of external factors: (i) the resisting forces, such as weight, tether force, or fluid drag for robots navigating inside wet environments and (ii) sliding friction forces that may result from sliding either forward or backward. In a previous work, we determined the mechanical energy requirement of worm robot locomotion over compliant surfaces, independently of the efficiency of the worm device. Analytical results were obtained by summing up the external work done on the robot and alternatively, by integrating the actuator forces over the actuator motions. In this paper, we present experimental results for an earthworm robot fitted with compliant contacts and these are post-processed to estimate the energy expenditure of the device. The results show that due to compliance, the COT of our device is increased by up to four-fold compared to theoretical predictions for rigid-contact worm-like locomotion.