If you are not happy with your results (and think you should have scored better), you can appeal one or more of your Leaving Cert results to the State Examinations Commission. In 2014, approximately 1 in 5 students that appeal results, received a higher grade [source].
On results day, when you get your results from your school or online you are given documentation which outlines the appeals process. You will receive an application form for viewing of scripts which allows you to look at your exam papers before making a decision on whether to appeal or not. You are entitled to bring one person along with you who may also view your scripts. The Organising Superintendent for the State Examinations Commission will assign a specific viewing session for each student.
After the leaving cert results come out in mid-August, you usually have about a week to apply to view your scripts. You get to view scripts at the end of August and within a few days you must decided whether to launch an appeal. The results of the appeals are usually released in Mid-October.
As of 2014, it costs €40 per subject to appeal (or €15.50 for Leaving Cert Applied) but if you happen to get a higher mark in any given subject, you get a refund on that subject.