The design, construction, and performance of a cross-coil double-resonance probe for solid-state NMR experiments on lossy biological samples at high magnetic fields are described. The outer coil is a Modified Alderman-Grant Coil (MAGC) tuned to the (1)H frequency. The inner coil consists of a multi-turn solenoid coil that produces a B(1) field orthogonal to that of the outer coil. This results in a compact nested cross-coil pair with the inner solenoid coil tuned to the low frequency detection channel. This design has several advantages over multiple-tuned solenoid coil probes, since RF heating from the (1)H channel is substantially reduced, it can be tuned for samples with a wide range of dielectric constants, and the simplified circuit design and high inductance inner coil provides excellent sensitivity. The utility of this probe is demonstrated on two electrically lossy samples of membrane proteins in phospholipid bilayers (bicelles) that are particularly difficult for conventional NMR probes. The 72-residue polypeptide embedding the transmembrane helices 3 and 4 of the Cystic Fibrosis Transmembrane Conductance Regulator (CFTR) (residues 194-241) requires a high salt concentration in order to be successfully reconstituted in phospholipid bicelles. A second application is to paramagnetic relaxation enhancement applied to the membrane-bound form of Pf1 coat protein in phospholipid bicelles where the resistance to sample heating enables high duty cycle solid-state NMR experiments to be performed.