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We have fabricated arrays of 60-nm-size magnetic Fe nanodots over a 1-cm2 -size area using nanoporous alumina membranes as shadow masks. The size and size distribution of the nanodots correlate very well with that of the membrane pores. By placing an antiferromagnetic FeF2 layer underneath the Fe nanodots, an exchange anisotropy can be introduced into the Fe/FeF2 system. We have observed an increase in the magnetic hysteresis loop squareness in biased nanodots, suggesting that exchange bias may be used as a tunable source of anisotropy to stabilize the magnetization in such nanodots.