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Recent research in quantum computation with superconducting qubits relies on SQUID magnetometers to distinguish the supercurrent states of the qubits. This poses a new challenge of demanding the measurement SQUID to introduce the least decoherence on the qubits during the measurement process. The SQUID is desired to operate in an unconventional way and be biased at currents significantly below the critical current level. This thesis lays the fundamental work of achieving the above by using the SQUID as a flux-sensitive inductor. The read-out relies on incorporating the SQUID inductor in a resonant circuit, and the state of the qubit is detected from the resonant frequency of the peak. A series of prototype resonant circuits were made from printed circuit boards and tested at room temperature. On-chip high-Q reso-nant circuits were designed to optimize the signals in the inductance measurements to about ten microvolts. Calculations of the decoherence times based on the spin-boson model were performed and the relaxation time falls in the microsecond regime