  We discuss the relaxation and dephasing rates that result from the control
and the measurement setup itself in experiments on Josephson persistent-current
qubits. For control and measurement of the qubit state, the qubit is
inductively coupled to electromagnetic circuitry. We show how this system can
be mapped on the spin-boson model, and how the spectral density of the bosonic
bath can be derived from the electromagnetic impedance that is coupled to the
qubit. Part of the electromagnetic environment is a measurement apparatus
(DC-SQUID), that is permanently coupled to the single quantum system that is
studied. Since there is an obvious conflict between long coherence times and an
efficient measurement scheme, the measurement process is analyzed in detail for
different measurement schemes. We show, that the coupling of the measurement
apparatus to the qubit can be controlled in situ. Parameters that can be
realized in experiments today are used for a quantitative evaluation, and it is
shown that the relaxation and dephasing rates that are induced by the
measurement setup can be made low enough for a time-resolved study of the
quantum dynamics of Josephson persistent-current qubits. Our results can be
generalized as engineering rules for the read-out of related qubit systems.
