Amorphous hydrogenated carbon (a-C:H) thin films are of great importance in a number of industrial applications due to their hardness, chemical stability, and optical transparency. In many applications, the thickness of the a-C:H film and/or its optical properties are critical for the performance of the complete structure, and, as a result, a means of measuring these quantities is important. In this work we review the use of spectroscopic ellipsometry and transmission measurements for the estimation of the thickness and optical constants of thin a-C:H films. Spectra are shown for films exhibiting Tauc effective bandgaps ranging from 0 - 2.3 eV. The films were prepared by magnetron sputtering and plasma CVD on both silicon and glass substrates. The general energy dependence of the a-C:H optical constants is discussed in terms of the absorption processes which occur in the film.