Belts and suspenders are both designed to hold up pants and should not be worn together. Not only is it redundant to do so, but it is a fashion mistake. Real Men Real Style, a men's fashion website, describes how the combination of belts and suspenders creates an unflattering rectangle on the torso.
Variations of modern suspenders, known as braces in British English, existed for 300 years prior to the invention of the modern style in 1820 by Albert Thurston. Their popularity was largely due to the fashionable high cut of men's pants at the time, which made belts impractical. The era of suspenders lasted until the 1930s, when men's wear once again accommodated belts.