PROC MODEL supports a variety of estimation methods which can be specified using options on the FIT statement. Most of the estimation methods do not use a log likelihood function in their formulation. However, for the FIML method, a log likelhood function is evaluated and is reported in the Estimation Summary Statistics table. You can read more about the FIML method used in PROC MODEL here:
http://documentation.sas.com/?docsetId=etsug&docsetVersion=14.2&docsetTarget=etsug_model_sect070.htm...
A log likelihood value is also used and reported when you specify your own likelihood using an 'errormodel ~ general' statement, or when you estimate a model using the t distribution.