Let X be a complex projective manifold and let D⊂Xβ→0ωβ2πβX\DωβωβX\DωβX\D(X,ωβ) be a smooth divisor. In this article, we are interested in studying limits when D⊂Xβ→0ωβ2πβX\DωβωβX\DωβX\D(X,ωβ) of Kähler–Einstein metrics D⊂Xβ→0ωβ2πβX\DωβωβX\DωβX\D(X,ωβ) with a cone singularity of angle D⊂Xβ→0ωβ2πβX\DωβωβX\DωβX\D(X,ωβ) along D. In our first result, we assume that D⊂Xβ→0ωβ2πβX\DωβωβX\DωβX\D(X,ωβ) is a locally symmetric space and we show that D⊂Xβ→0ωβ2πβX\DωβωβX\DωβX\D(X,ωβ) converges to the locally symmetric metric and further give asymptotics of D⊂Xβ→0ωβ2πβX\DωβωβX\DωβX\D(X,ωβ) when D⊂Xβ→0ωβ2πβX\DωβωβX\DωβX\D(X,ωβ) is a ball quotient. Our second result deals with the case when X is Fano and D is anticanonical. We prove a folklore conjecture asserting that a rescaled limit of D⊂Xβ→0ωβ2πβX\DωβωβX\DωβX\D(X,ωβ) is the complete, Ricci flat Tian–Yau metric on D⊂Xβ→0ωβ2πβX\DωβωβX\DωβX\D(X,ωβ). Furthermore, we prove that D⊂Xβ→0ωβ2πβX\DωβωβX\DωβX\D(X,ωβ) converges to an interval in the Gromov–Hausdorff sense.