Next to the city administration was the estate of the Zvorikins, one of the most famous families in Murom. To distinguish between different branches of this family, they were given nicknames. For example, there were the Zvorikins of the Hills, Zvorikins of the Anchors, Zvorikins the Weavers, and Zvorikins the Iron. Those in question were called Kozomorovs, although the origin of this nickname is unknown.

The estate included a large stone residential house, two wings, a stable, a stone tent, and various wooden outbuildings. The courtyard was completely enclosed, and an extensive fruit orchard spread along the slope of the ravine. The house was built in the second half of the 1840s by Kuzma Dmitrievich Zvorikin, the great-grandfather of television inventor Vladimir Zvorikin. Documents indicate that in the early 1840s, Kuzma Dmitrievich gradually purchased land on the edge of the Nikol-Zaryadskiy ravine, where the Zvorikins' urban estate later emerged.

The main residential building is designed in the classical style and faces the trading square. Vladimir Zvorikin fondly recalls his childhood in this house: "The house where I was born belonged to our family for several generations. It was a large three-story stone building, too big even for our numerous family. We only occupied the second floor, the rest of the house was empty, and we, the children, had plenty of space to play hide and seek."

In 1918, the Zvorikins' mansion was transferred to the city museum, and since then it has housed historical and artistic exhibitions. Since 2010, the building has been closed for renovation.