The nanopore is a powerful tool for probing biomolecular interactions at the single-molecule level, and shows great promise commercially as a next-generation deoxyribonucleic acid (DNA) sequencing technology. Coupling active voltage control with the nanopore has expanded its capabilities, for example, by allowing precise manipulation of DNA-enzyme complexes at millisecond timescales. However, any change in voltage excites capacitance in the system and results in masking the molecule's contribution to the measured current. To improve active control capabilities, a method is needed for continuous monitoring of the molecule's contribution to the current during voltage-varying experiments. The method must be able to separate the capacitive effects from the channel conductance, which is the parameter that can be used to infer the state of the molecule in the pore. The contributions of this paper are: 1) to develop a dynamic model of the nanopore instrument which includes capacitance and conductance parameters and 2) to develop model-based algorithms for estimating the conductance parameter during voltage varying experiments. First, grey- and black-box state-space models are estimated and compared using nanopore experimental data and system identification tools. Next, a validated grey-box model is used to derive two methods for estimating the channel conductance under voltage-varying conditions: one based on least-squares, and one based on the extended Kalman filter. In simulations and experiments, the Kalman filter outperforms the simpler least-squares method.