We demonstrate a technique of broadband spin torque ferromagnetic resonance (ST-FMR) with magnetic field modulation for measurements of spin wave properties in magnetic nanostructures. This technique gives great improvement in sensitivity over the conventional ST-FMR measurements, and application of this technique to nanoscale magnetic tunnel junctions (MTJs) reveals a rich spectrum of standing spin wave eigenmodes. Comparison of the ST-FMR measurements with micromagnetic simulations of the spin wave spectrum allows us to explain the character of low-frequency magnetic excitations in nanoscale MTJs.The following article appeared in Appl. Phys. Lett. 103, 172406 (2013) and may be found at http://dx