This paper introduces a method to automatically estimate vertical and horizontal clearances of highway viaducts and gantries from Mobile Laser Scanner (MLS) point clouds. It is essential to have accurate data on the vertical and horizontal clearances of overhead infrastructure objects along the highway. Accurate clearance data is used for routing oversized transports, infrastructure reconstruction, maintenance and settling legal claims after incidents. The proposed method takes a point cloud of an infrastructure object as input, and as output provides the user with a concise overview of the horizontal and vertical clearances of the object. A point cloud of a highway overpass or gantry is segmented into the different clusters relevant for determining the clearances. The discrete points in these clusters will then be used to approximate their surfaces with B-splines. Subsequently the minimal clearances can be estimated. These clearances are estimated at certain pre-specified locations according to guidelines from the highway authority. The paper also includes a comparison of the inferred clearances from the point clouds with archived measurements performed by third party contractors. For this case study, a Dutch highway section containing 50 gantries and 20 viaducts is selected. Along this stretch of highway the clearances are estimated. The estimated clearances for each structure are then compared with archived in situ measurements. This will give a quantitative analysis of the quality of the estimated clearances. The estimated vertical clearances have an overestimation of 20-30 mm compared to the validation data. The horizontal clearances show a median underestimation of 20 mm.