do you want to measure translation of a single transcript and corresponding peptide, or global translation? For global translation there is AHA (methionine analog) and OPP-puromycin labeling kits that use 'click-chemistry' reaction to attach a label for visualization of protein synthesis.
alternatively, if you want to look at translation of single proteins, there is a SILAC-MS/MS approach, as well as a a fluorescent imaging method. below are the papers describing these methods.
Immunological techniques, such as Western blot or ELISA. You need an antibody specific for that protein. To make such an assay quantitative, you should have a standard, which is the purified protein.
If it is an enzyme with an activity that is very specific, then you might be able to do an enzyme activity assay.