A bstract The cross-sections of exclusive (coherent) photoproduction J/ψ and ψ (2S) mesons in ultra-peripheral PbPb collisions at a nucleon-nucleon centre-of-mass energy of 5 . 02 TeV are measured using a data sample corresponding to an integrated luminosity of 228 ± 10 μb − 1 , collected by the LHCb experiment in 2018. The differential cross-sections are measured separately as a function of transverse momentum and rapidity in the nucleus-nucleus centre-of-mass frame for J/ψ and ψ (2S) mesons. The integrated cross-sections are measured to be $$ {\sigma}_{J/\psi}^{\textrm{coh}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>σ</mml:mi> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:mrow> <mml:mi>coh</mml:mi> </mml:msubsup> </mml:math> = 5 . 965 ± 0 . 059 ± 0 . 232 ± 0 . 262 mb and $$ {\sigma}_{\psi (2S)}^{\textrm{coh}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>σ</mml:mi> <mml:mrow> <mml:mi>ψ</mml:mi> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>S</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mi>coh</mml:mi> </mml:msubsup> </mml:math> = 0 . 923 ± 0 . 086 ± 0 . 028 ± 0 . 040 mb, where the first listed uncertainty is statistical, the second systematic and the third due to the luminosity determination. The cross-section ratio is measured to be $$ {\sigma}_{\psi (2S)}^{\textrm{coh}}/{\sigma}_{J/\psi}^{\textrm{coh}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>σ</mml:mi> <mml:mrow> <mml:mi>ψ</mml:mi> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>S</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mi>coh</mml:mi> </mml:msubsup> <mml:mo>/</mml:mo> <mml:msubsup> <mml:mi>σ</mml:mi> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:mrow> <mml:mi>coh</mml:mi> </mml:msubsup> </mml:math> = 0 . 155 ± 0 . 014 ± 0 . 003, where the first uncertainty is statistical and the second is systematic. These results are compatible with theoretical predictions.