Most often researchers will use simple ELISAs or other immunoassay formats to check for antibody expression. These methods require relatively commonplace equipment and reagents, but can take longer to get to results. For serum and protein free media, if your antibody titers are high, you can actually get a relatively accurate look at antibody concentrations by running a simple Bradford assay since most of the protein in the cultures will be your antibody of interest. Lastly, there are high-end, label-free instruments such as the ForteBio Octet that can quantify antibody titers using Protein A sensors or similar.