Currently, the access to the knowledge of stiffness values is typically constrained to a-priori identified models or datasheet information, which either do not usually take into account the full range of possible stiffness values or need extensive experiments. This work tackles the challenge of stiffness estimation in articulated soft manipulators, and it proposes an innovative solution adding value to the previous research by removing the necessity for force/torque sensors and generalizing to multi-degree-of-freedom robots. Built upon the theory of unknown input-state observers and recursive least-square algorithms, the solution is independent of the actuator model parameters and its internal control signals. The validity of the approach is proven analytically for single and multiple degree-offreedom robots. The obtained estimators are first evaluated via simulations on articulated soft robots with different actuations and then tested in experiments with real robotic setups using antagonistic variable stiffness actuators.