In this paper, we introduce the notion of the structured phase margin for characterising stability margins for a dynamical system with block-structured phase uncertainty. Since the structured phase margin may in general be difficult to compute, we derive an easily computable lower bound in terms of a generalised eigenvalue problem. This bound is constructed by choosing stability multipliers that are tailored to the structure of the phase uncertainty. The results in this paper complement and generalise phase information results presented in the literature involving principal phases, multivariable phase margin, phase spread, phase envelope, phase matching, and phase-sensitive structured singular value. Finally, using the structured phase margin, we present new and improved delay-dependent stability criteria for stability analysis of time-delay systems.