We describe an experiment in which a scanning tunneling microscope (STM) is employed to selectively contact a lithographically fabricated structure at 350 mK. The STM enables us to probe the structure, a Josephson-junction array, at various positions. The experiment demonstrates that it is possible to combine the use of a scanning tunneling microscope with transport measurements on lithographically fabricated structures at temperatures below 1 K. We focus on the strategy to position the tip above the structure of interest, the influence of the STM on the electronic noise, and on the effective temperature of the sample.