Series-elastic actuation (SEA) is widely employed on hopping robots due to its capability to diminish energy consumption and peak torque requirements. However, scant attention has been given in existing studies to the jump height achieved by robots utilizing SEA. To maximise jump height while retaining SEA’s benefits, a solution to improve the actuator involves having a variable mechanical advantage (MA) gearbox between the elastic element and the end-effector. Continuously variable transmission (CVT) can produce such a precise MA profile with relatively straightforward structures. Although previous studies have incorporated CVT in robotics, with a predominant focus on wheeled robots, the potential advantages of using CVT on jumping robots have been overlooked. In this study, mathematical modelling is utilized to simulate and analyse the advantages of having a CVT-enhanced SEA (C-SEA) in terms of achieving higher jumps and protecting structural integrity for hopping robots. The results indicate that the C-SEA manages to reduce the peak ground reaction force by approximately \(50\%\) compared to the regular SEA. Moreover, C-SEA demonstrates superior performance in most cases with higher motor rotor mass and viscous damping coefficient when actuated by a motor with linear behaviour.