Silver and gold films with thicknesses in the range of 120– $450\mathrm{nm}$ were evaporated onto glass substrates. A sequence of slits with widths varying between 70 and $270\mathrm{nm}$ was milled in the films using a focused gallium ion beam. We have undertaken high-resolution measurements of the optical transmission through the single slits with $488.0\mathrm{nm}$ (for Ag) and $632.8\mathrm{nm}$ (for Au) laser sources aligned to the optical axis of a microscope. Based on the present experimental results, it was possible to observe that (1) the slit transmission is notably affected by the film thickness, which presents a damped oscillatory behavior as the thickness is augmented, and (2) the transmission increases linearly with increasing slit width for a fixed film thickness.