The field of quantum computing with superconducting qubits has achieved considerable success, yet the challenge of realizing high-fidelity multi-qubit operations remains central to its advancement. Fluxonium qubits, with their long coherence times and strong anharmonicity, are promising building blocks for such systems. In this thesis, we present the two-fluxonium gate implementations we worked on, with a particular focus on the first realization of a cross-resonance CNOT gate with a capacitively coupled two-fluxonium system in a 3D cavity. This fully microwave-driven gate scheme confines qubit dynamics within the computational space and preserves coherence while enabling high-fidelity operations. We present our experimental results that achieve two-fluxonium gate fidelities up to 99.5% despite challenging setup conditions. Our findings suggest pathways for further reducing the error rates, with implications for future research into more efficient quantum gate implementations.