The precise implementation and manipulation of quantum gates is key to extracting advantages from future quantum technologies. Achieving this requires very accurate control over the quantum system. If one has complete knowledge about a Hamiltonian, accurate manipulation of the system is possible. However, in real scenarios, there will often be some uncertainty in the parameters of the Hamiltonian, which makes full control of the system either difficult or impossible. In this paper we consider two model Hamiltonians with a continuous parameter that is partly unknown. We assess robust controllability against this parameter uncertainty using existing theoretical frameworks and take a numerical route by discretizing the unknown parameter in the cases where we cannot predict controllability. Furthermore, we introduce a penalty term into the fidelity function to optimize control pulses, enhancing robustness against the influence of parameter fluctuations. Within our framework, we analyze the qualitative differences in the robust controllability of the two systems.