The flux of cosmic ray magnetic monopoles at the earth's surface is measured using a superconducting induction detector. The detector employs gradiometer twisted loop configurations within completely closed superconducting shields to obtain a large sensitive area and stable operation in ~1-10 mGauss ambient magnetic fields. The detector is isolated from the environment to inhibit the production of spurious signals and the environment is monitored in order to veto such signals. The total sensitive area for a monopole passing through either or both of the gradiometers is 2100 cm^2. In two exposure periods, (19 days with only 1400 cm^2 sensitive area and 136 days with 2100 cm^2), there were no monopole candidates observed. A monopole flux limit of fm ~< 6.7 x 10^-12 cm^-2 sr^-1 sec^-1 at 90% Confidence Level is therefore established. The design and performance of a second generation detector with 1.1 meter diameter gradiometers is also presented. The detector demonstrates that gradiometers can be overlapped without inductive coupling to obtain high redundancy without increasing shield volume. The detector was operated in ambient magnetic fields of ~5-125 mGauss. The rate of occurrence of two-fold coincident monopole-sized d.c. offsets is measured to be less than 1 per 500 years. Implications for 100 m^2 to 1000 m^2 induction detectors are discussed.