Using a solid-state nanopore to measure the concentration of clinically relevant target analytes, such as proteins or specific DNA sequences, is a major goal of nanopore research. This is usually achieved by measuring the capture rate of the target analyte through the pore. However, progress is hindered by sources of systematic error that are beyond the level of control currently achievable with state-of-the-art nanofabrication techniques. In this work, we show that the capture rate process of solid-state nanopores is subject to significant sources of variability, both within individual nanopores over time and between different nanopores of nominally identical size, which are absent from theoretical electrophoretic capture models. We experimentally reveal that these fluctuations are inherent to the nanopore itself and make nanopore-based molecular concentration determination insufficiently precise to meet the standards of most applications. In this work, we present a simple method by which to reduce this variability, increasing the reliability, accuracy, and precision of single-molecule nanopore-based concentration measurements. We demonstrate controlled counting, a concentration measurement technique, which involves measuring the simultaneous capture rates of a mixture of both the target molecule and an internal calibrator of precisely known concentration. Using this method on linear DNA fragments, we show empirically that the requirements for precisely controlling the nanopore properties, including its size, height, geometry, and surface charge density or distribution, are removed while allowing for higher-precision measurements. The quantitative tools presented herein will greatly improve the utility of solid-state nanopores as sensors of target biomolecule concentration.