We demonstrate that a continuously measured microelectronic circuit, the Cooper-pair box measured by a radio-frequency single-electron transistor, approximates a quantum two-level system. We extract the Hamiltonian of the circuit through resonant spectroscopy and measure the excited-state lifetime. The lifetime is more than 10(5) times longer than the inverse transition frequency of the two-level system, even though the measurement is active. This lifetime is also comparable to an estimate of the known upper limit, set by spontaneous emission, for this circuit.