Wavefront synthesis is a central objective in many applications of programmable metasurfaces (PMs), ranging from electromagnetic holography and computational imaging to massive backscatter communications. Yet, fundamental limits on the ability of a given real-world PM prototype to synthesize a desired output wavefront remain largely unknown. Here, we derive prototype-aware and electromagnetically consistent bounds on target-wavefront synthesis in reconfigurable MIMO wave systems whose programmability stems from tunable lumped elements. Our approach combines multiport network theory (MNT), experimentally estimated proxy MNT parameters, and semidefinite relaxation. We account for relevant practical aspects of typical real-world PMs, such as mutual coupling, binary programmability, and lossy tunable loads. We derive bounds on strength-agnostic wavefront-synthesis fidelity, shape-agnostic target-mode strength, and the strength--fidelity Pareto frontier using two complementary threshold sweeps. We evaluate these bounds for four experimental MIMO systems whose transfer functions are parametrized by a reconfigurable intelligent surface (RIS), involving up to 100 1-bit-programmable elements and radio environments ranging from rich scattering to free space. Our bounds yield practical insights such as the identification of unattainable performance regions and the close-to-optimality certification of certain optimization outcomes. Comparisons with feasible discrete-optimization benchmarks show that the bounds can often be closely approached in practice, indicating tightness. While demonstrated with a RIS prototype, our methodology applies broadly to lumped-element-reconfigurable wave systems, including dynamic metasurface antennas. Altogether, this work contributes to the development of a prototype-aware electromagnetic information theory for reconfigurable wave systems.