This paper focuses on evaluating three model order reduction (MOR) methods applied to reducing the order of high-order digital filters. These methods are the Balanced Truncation (BT), the Modal Truncation (MT), and the Balanced Stochastic Truncation (BST). The authors used these algorithms to reduce the order of a 6th-order IIR filter to orders 2, 3, and 4. The results, based on the deviation between the original and reduced systems according to the norms and the relative error, show that the BT and BST algorithms yield minimal reduction errors. The frequency and time domain response plots are nearly identical between the original and reduced systems. Thus, these two methods can be used for reducing the order of IIR filters. However, the MT algorithm results in significant errors, and the impulse response plots in both the time and frequency domains show substantial discrepancies between the original and reduced systems. Therefore, applying the MT algorithm to digital filter design has many drawbacks.