We propose a model-independent framework for fitting hadronic form-factor data, which is often only available at discrete kinematical points, using parameterisations based on to unitarity and analyticity. In this novel approach the latter two properties of quantum-field theory regulate the ill-posed fitting problem and allow model-independent predictions over the entire physical range. Kinematical constraints, for example for the vector and scalar form factors in semileptonic meson decays, can be imposed exactly. The core formulae are straight-forward to implement with standard math libraries. We take account of a generalisation of the original Boyd Grinstein Lebed (BGL) unitarity constraint for form factors and demonstrate our method for the exclusive semileptonic decay B s → K ν, for which we make a number of phenomenologically relevant predictions, including the CKM matrix element |V ub |.