In this paper we present universal broadband multiresonator quantum memory based on the spatial-frequency combs of the microresonators coupled with a common waveguide. We find a Bragg-type impedance matching condition for the coupling of the microresonators with a waveguide field that provides an efficient broadband quantum storage. The analytical solution obtained for the microresonator fields enables sustainable parametric control of all the memory characteristics. We also construct an experimental prototype of the studied quantum memory in the microwave spectral range that demonstrates basic properties of the microwave microresonators, their coupling with a common waveguide, and independent control of the microresonator frequencies. Experimentally observed narrow lines of the microresonators confirm the possibility of multiresonator quantum memory implementation.