Hit the "Tilde" (~) key to enter the console and type in these commands. You can save time by typing just "Mouse" and hitting tab to find them.
Don't worry about Mouse Smoothing, as it's disabled by default.

If you want to have the same sensitivity as in Source or IDTech engine games, then use use the conversion calculator on https://www.mouse-sensitivity.com/ to find the right value. Simply enter in the same value you would use in one of those games and it will tell you the correct value for Serious Sam HD, including the number of centimeters for a 360° rotation. You can gain even more aiming precision by changing the FOV to match your monitor's aspect ratio.

Thank you for reading this guide. I'd like to credit "repzor" from the Seriously! community for his post which inspired me to look up the exact commands and post them here. I'd also like to credit CinemaBlend for the thumbnail preview image I used.

This guide will also work for The Second Encounter as well.