Assessing the run-up arising from ocean waves as they reach a coastal or offshore structure is an important aspect of engineering projects. By combining formulations for calculating the run-up of regular waves with wave statistical descriptions, a procedure is implemented to assess wave run-up in random sea conditions. This procedure uses the First and Second Order Reliability Methods. It is applied to four cases representing common coastal structures: vertical wall, vertical cylinder, smooth impermeable slope and rough permeable slope. The results of the reliability methods are compared with two other methodologies commonly used in coastal and ocean engineering. The first methodology (Method I) consists of calculating the significant wave height for a given return period from the long-term distribution of storms. Then, the maximum wave height corresponding to the significant wave height, and its corresponding wave run-up are obtained. Method II consists of obtaining a long-term distribution of individual wave heights, so that the maximum wave height for a given return period can be directly calculated. Then, the corresponding wave run-up is determined as in Method I, by applying regular wave formulations to the maximum wave height. Method I provides lower values of wave run-up than all other methods, while Method II provides the highest values of wave run-up, and proves to be dependent on the severity factor, a parameter characterizing the long-term distribution of storms. Results show that both the First and Second Order Reliability Methods correspond with Method II when the values of the severity factor are low, but approach Method I as the value of the severity factor increases. The wave run-up is found to depend on the characteristics of the structure in place, such as cylinder radius, slope angle and surface permeability, as well as on such sea conditions as severity factor and the duration and frequency of storms. The wave run-up to significant wave height ratio is independent of the return period for the four cases studied here. This ratio results in a non-dimensional form of wave run-up that appears to provide useful means for describing the phenomenon.