The pseudospectra is a useful tool to study the behavior of systems associated with nonnormal matrices. Different projection Krylov methods have been used to calculate the pseudospectra of large matrices rather than typical aproaches which require the application of SVD descomposition several times, inverse power method or Lanczos method. In this work we investigate practical applicability and performance of new projection approaches to approximate the pseudospectrum of large matrices. Specifically we compare Block Implicit restarted Arnoldi method (BLIRAM) and the Implicit Unsimmetric Lanczos with other projection schemes. As a complement we study the computation of matrices pseudospectrum in an energy or weighted norm, developing a practical method to convert an Arnoldi fatorization based on the Euclidian inner product into another Arnoldi factorization in a weighted inner product. Applying this method we are able to approximate the pseudospectrum of large matrices in the weighted norms in an efficient form.