It is well known that any equivalence in a 2-category can be upgraded to an adjoint equivalence. I will present an analogous result for Batanin-Leinster weak ω-categories. More precisely, I will introduce two notions of "coherent equivalence" such that 1) any equivalence in a weak ω-category can be upgraded to such a coherent one, and 2) the free coherent equivalence n-cells can be used to characterise a weak ω-categorical version of isofibrations via the right lifting property. As a bonus, we also obtain an explicit description of the fibrations between strict ω-categories in the Lafont-Métayer-Worytkiewicz folk model structure. This talk is based on joint work with Soichiro Fujii (National Institute of Informatics) and Keisuke Hoshino (Kyoto University).