The implantation of low energy polarized positive muons (μ+) with energies between 0.5 and 30 keV in thin (<100 nm) Al, Cu, Ag, and Au films sputtered onto quartz glass substrates has been studied by using a muon spin rotation technique. The fraction of muons stopped in the metal was determined by measuring the energy dependence of the μ+ decay asymmetry which is essentially proportional to the fraction of μ+ stopping in the metal layer. From this quantity also the backscattering probability from the metallic layer can be obtained. The results are compared with predictions of implantation profiles of muons obtained with the TRIM.SP and SRIM2000 Monte Carlo codes. The applicability of these simulations to predict the interaction of low energy muons in matter and observed differences with the experimental data are discussed.