A hadron resonance gas model including all known particles and resonances with masses m < 2 GeV and an exponentially rising density of Hagedorn states for m > 2 GeV is used to obtain an upper bound on the shear viscosity to entropy density ratio, eta/s approximately 1/(4pi), of hadronic matter near Tc. We found a large trace anomaly and small speed of sound near Tc, which agree well with recent lattice calculations. We comment on the bulk viscosity to entropy density ratio close to Tc.