The Constitution prevents the President of the United States from pardoning himself. He cannot use his power to prevent his impeachment or removal. Now, some will argue that the Judicial Branch cannot indict a sitting President. This is true, however...
The Judicial Branch and/or House Judiciary Committee can order a special council to investigate suspected hinky business committed by the sitting President. Once this special council is ready to submit their findings to the House Judiciary Committee, they will then do so. The Committee can then determine if the findings are enough to bring up Articles of Impeachment to the House floor for a vote.
If Articles are deemed warranted, they are then voted on by the House. If the House votes to impeach, the matter is then sent to the Senate.
The Senate then serves as judge and jury. They determine in the impeachment holds water (just like a normal court will hear charges and determine if an indictment holds water). If they find they do, they can then vote to remove the President from office.
At this point, the President is no longer the sitting President, and...depending on what they were removed for...could then potentially be indicted on any and all crimes he was found to have committed that caused his impeachment!! And thus...no longer having their pardon power...they cannot pardon themselves from any convictions after the fact, either!
Now, some may ask about these cases that courts have determined can be heard that are not related to the ongoing special council investigation. Well, these cases involve civil actions...and no one is immune from a civil action. Keep in mind that the President can only be in office for so long. Most statutes of limitations only affect how long a person has to make a filing on a wrong done to them. The court, however, can continue the case as long as needed. Civil cases do not fall under the same rules as criminal cases, where the court must hear and try a case in a certain amount of time as protection of the rights of the accused...mostly because many of these folks are held until trail. You cannot hold a person in jail indefinitely for an accused crime without making a conviction. Civil judgements are a completely different ball game!