We have studied the superconducting T c (H ) phase boundary of an Al superconducting disk with a perpendicularly magnetized dot on top of it. We used cylindrical and triangular dots. The inhomogeneous stray fields generated by these dots strongly affect the T c (H ) line, which now has the highest T c at a finite applied field. This 'magnetic bias' of the T c (H ) phase boundary depends on the magnetization of the dots. The field inhomogeneity leads to a pronounced modification of the T c (H ) periodicity. The theoretical T c (H ) dependence, calculated in the framework of the Ginzburg-Landau theory, fits our experimental data very well. In a superconducting Pb film with a lattice of Co/Pd magnetic dots, field-induced superconductivity has been investigated. This remarkable effect appears due to the compensation of the returning stray fields of the dots by the applied magnetic field. As a result of the field compensation, the total field under the dots is enhanced, whereas in the areas between the dots the total field is strongly reduced, thus causing the field-induced superconductivity to appear.