Branched open-circuit lines are introduced for artificial negative-permittivity media, which is a type of metamaterial, to simultaneously achieve compact unit cells and adjustable bandgaps to cover multiband frequencies. Our electromagnetic bandgap (EBG) structures, the unit cells of which are under $1/26$ of the wavelength in a substrate, were designed to display characteristic effects, including bandgap-separation control and enhancement of the bandgap width. We analytically and experimentally investigated these effects. The compactness is derived from the length-dependent resonances of the open-circuit line instead of inductance-capacitance resonances, and the adjustable bandgaps originate from the introduction of the branched shape, which destroys the periodic capactive-inductive-impedance alternation of not-branched open-circuit lines. The proposed EBG structures are highly promising for frequency-selective devices, such as for electromagnetic noise suppression in power distribution networks.