The reconstruction of evolutionary trees is one of the primary objectives in phylogenetics. Such a tree represents historical evolutionary relationships between different species or organisms. Tree comparisons are used for multiple purposes, from unveiling the history of species to deciphering evolutionary associations among organisms and geographical areas. In this paper, we describe a general method for comparing phylogenetic trees and give some basic properties of the Matching Split metric, which is a special case of a general definition. We focus on four metrics for binary unrooted trees. We present results of a computational experiment concerning an application of those metrics to estimating the quality of a phylogenetic signal.