Process for coating a component comprising a surface comprising cooling fluid openings which adjoin cooling fluid channels in the interior of the component, wherein the process comprises the following steps: a) introduction of the component into an apparatus for the surface analysis of the component, where the apparatus comprises at least two measuring devices and at least one fastening for the component, where the fastening is suitable for being connected detachably either directly or indirectly to the component, where the apparatus is suitable for carrying out a two-part surface analysis, where the position of the cooling fluid openings on the surface of the component is determined in one part of the surface analysis and where the three-dimensional shape of at least one cooling fluid opening is determined in another part of the surface analysis, where at least one element from the group consisting of the at least two different measuring devices and the at least one fastening is movable, b) carrying out of the surface analysis of the component, where data in respect of the position of the cooling fluid openings on the surface of the component and in respect of the three-dimensional shape of at least one cooling fluid opening are detected, c) application of a coating to the component, where the cooling fluid openings are at least partly, preferably completely, closed, d) removal of the coating in the region of the cooling fluid openings by means of the data obtained in step b), where the two parts of the two-part surface analysis are carried out using the different measuring devices. a) introduction of the component into an apparatus for the surface analysis of the component, where the apparatus comprises at least two measuring devices and at least one fastening for the component, where the fastening is suitable for being connected detachably either directly or indirectly to the component, where the apparatus is suitable for carrying out a two-part surface analysis, where the position of the cooling fluid openings on the surface of the component is determined in one part of the surface analysis and where the three-dimensional shape of at least one cooling fluid opening is determined in another part of the surface analysis, where at least one element from the group consisting of the at least two different measuring devices and the at least one fastening is movable, where the apparatus comprises at least two measuring devices and at least one fastening for the component, where the fastening is suitable for being connected detachably either directly or indirectly to the component, where the apparatus is suitable for carrying out a two-part surface analysis, where the position of the cooling fluid openings on the surface of the component is determined in one part of the surface analysis and where the three-dimensional shape of at least one cooling fluid opening is determined in another part of the surface analysis, where at least one element from the group consisting of the at least two different measuring devices and the at least one fastening is movable, b) carrying out of the surface analysis of the component, where data in respect of the position of the cooling fluid openings on the surface of the component and in respect of the three-dimensional shape of at least one cooling fluid opening are detected, c) application of a coating to the component, where the cooling fluid openings are at least partly, preferably completely, closed, d) removal of the coating in the region of the cooling fluid openings by means of the data obtained in step b), where the two parts of the two-part surface analysis are carried out using the different measuring devices.