Effective treatment of unbounded domains using artificial truncating boundaries are essential in numerical simulation including unbounded media, such as in the scope of exterior acoustics, sound transmission calculations,... Among these, Perfectly Matched Layers (PML) have proved to be particularly efficient and flexible, as well as relatively easy to implement using the Finite Element Method (FEM). However, an efficient handling of frequency sweeps is not trivial with such absorbing layers since the formulation inherently contains coupled space- and frequency-dependent terms. Using the FEM, this may imply generating system matrices at each step of the frequency sweep. In this contribution, an approximation is presented in order to allow for efficient frequency sweeps, for instance using Pade-based methods as extensively used by the authors in previous contributions. The performance and robustness of the proposed approximation is presented on an acoustic cases. A generic, robust way to truncate the acoustic domain efficiently is also proposed, tested on a range of test cases and for different frequency regions. It is shown that the approximation, based on a sub-interval approximation of a tuning parameter in the frequency range of interest, provides consistently very good results, close to the costly, original formulations. An a priori estimate of a robust choice for this tuning parameter is also introduced, together with a set of empirical recommendations associated with mesh size, domain size and truncation.