In this talk I will present a series of techniques to automatically compute parametric certificates of dynamic memory utilization for Java like programs. Core to these techniques is the utilization of program invariants which are used as a mean to approximate visits to memory consuming statements and to bind information provided by the different methods of the application under analysis. The approach is implemented in a prototype tool that allows us to experimentally evaluate the efficiency and accuracy of the method on several Java benchmarks with encouraging results. I will pinpoint some challenges we have to face during the implementation of these techniques and I will discuss what we think are the advantages and limitations of our approach.