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The LHC collimation upgrade foresees two additional collimators installed in the dispersion suppressor regions of points 2, 3 and 7. To obtain the necessary longitudinal space for the collimators, a solution based on an 11 T dipole as replacement of the 8.33 T LHC main dipoles is being considered. CERN and FNAL have started a joint development program to demonstrate the feasibility of technology for this purpose. The program started with the development and test of a 2-m-long single-aperture demonstrator magnet. The goal of the second phase is the design and construction of a series of 2-m-long twin-aperture demonstrator magnets with a nominal field of 11 T at 11.85 kA current. This paper describes the electromagnetic design and gives a forecast of the field quality including saturation of the iron yoke and persistent-current effects in the coils. The mechanical design concepts based on separate collared coils, assembled in a vertically split iron yoke are also discussed.