The intercalation of epitaxial graphene on SiC(0001) with Ca has been studied extensively, yet precisely where the Ca resides remains elusive. Furthermore, the intercalation of Mg underneath epitaxial graphene on SiC(0001) has not been reported. Here, we use low energy electron diffraction, X-ray photoelectron spectroscopy, secondary electron cutoff photoemission, and scanning tunneling microscopy to elucidate the physical and electronic structures of both Ca- and Mg-intercalated epitaxial graphene on 6H-SiC(0001). We find that Ca intercalates underneath the buffer layer and bonds to the Si-terminated SiC surface, breaking the C-Si bonds of the buffer layer, i.e., "freestanding" the buffer layer to form Ca-intercalated quasi-freestanding bilayer graphene (Ca-QFSBLG). The situation is similar for the Mg-intercalation of epitaxial graphene on SiC(0001), where an ordered Mg-terminated reconstruction at the SiC surface is formed and Mg bonds to the Si-terminated SiC surface are found, resulting in Mg-intercalated quasi-freestanding bilayer graphene (Mg-QFSBLG). Ca-intercalation underneath the buffer layer has not been considered in previous studies of Ca-intercalated epitaxial graphene. Furthermore, we find no evidence that either Ca or Mg intercalates between graphene layers. However, we do find that both Ca-QFSBLG and Mg-QFSBLG exhibit very low work functions of 3.68 and 3.78 eV, respectively, indicating high n-type doping. Upon exposure to ambient conditions, we find Ca-QFSBLG degrades rapidly, whereas Mg-QFSBLG remains remarkably stable.