Solidly mounted (SMR-type) thin film bulk acoustic resonators operating at 2.2, 4.1, and 8.0 GHz and with lateral extents from 30 to 500 microm were fabricated and their performance as mass sensors was evaluated theoretically as well as experimentally. It was found that increasing the frequency leads to a principally improved performance of these devices. Problems arising for the horizontal as well as the vertical dimension and structure are investigated.