Continuous-time system identification has primarily dealt with sampled input and output data for constructing continuous-time models. However, sampled signals can lead to inaccurate models if their intersample behavior is not addressed appropriately. In this paper, this effect is explored in detail with respect to the SRIVC and CLSRIVC estimators, which are some of the most popular methods for open and closed-loop continuous-time system identification respectively. Based on our consistency analysis, we propose an algorithm that alleviates the asymptotic bias of these methods for arbitrary input excitations and provide an alternative procedure to achieve consistent estimates for band-limited signals. Simulation examples show the effectiveness of our approach.