Mathematical models of physical systems often have parameters that must be estimated from measured data. Inestimable models have more parameters than can be estimated from available data. In this work, a method for identifying inestimable parameters or parameter combinations is proposed. The method is based on partitioning the parameter space into estimable and inestimable subspaces. Parameter combinations in the inestimable subspace have little effect on measured values and can therefore be fixed at a nominal value. The number of effective parameters is thereby reduced to the dimension of the estimable subspace. The proposed method is applicable over a range of experimental conditions. Detailed examples, including a batch bioreactor and a three-phase reactor system, are included for illustration.