The true pomp and circumstance surrounding the peerage began during the reign of Henry VIII, when the Sovereign introduced several innovations in courtly procedure from France. However, local traditions were always different from those at court. Upon the death of an heir and the succession of his heir apparent, the new heir would have likely held some sort of local banquet or festival to celebrate their newly achieved prominence. They would have also met the local gentry and clergy, all of whom would have likely offered their best wishes for a long life. However, there was no official "coronation" per se anywhere in the British Isles. There were three major reasons for this:

a) Coronations are reserved for sovereigns, which symbolized their right to rule -- originally with the sanction of the Pope -- over their realm by divine right as given to them by God

b) Peers who were powerful enough to hold some sort of quasi-coronation would have found themselves squarely in the sights of the Crown as a possible claimant to the "big boy" throne

c) Depending on the era, most of the peers would have consisted of close relatives of the reigning Sovereign

In contrast to local celebrations, celebrations at court were much more formal. The major definition of what constitutes a peer is his writ of summons to parliament, during which time the Sovereign would personally "introduce" the peer to the House of Lords. Once the House of Lords became more "clubby" under Charles II, peers were no longer introduced this way unless they were new creations. This ceremony would have been the closest thing to a coronation that a Medieval peer would have had at his disposal.

Having said that, there are massive exceptions to the above. Marcher lords were considered to rule sicut regale -- "like that of a king" -- and they may have had coronation ceremonies. They also had exceptional privileges such as building castles and granting amnesty. The great feudal earls of Scotland may have had quasi-coronations although that is likewise outside the scope of your question.

On a last note, an important thought: we tend to think of peers today as the "end all be all" of Medieval and Tudor England. However, there were a number of untitled magnates who lived in a fashion that would have rivaled many of their titled compatriots. Most of these men were created knights generation after generation in order to avoid challenging the power of the Crown because kings were somewhat wary of the power of the peerage after the Magna Carta. This is why families like the Grosvenors, who play an extremely important part in early Welsh history, weren't made peers until the 17th century when the Crown had to start giving away major concessions to ensure its long-term survival.

A great primary source for all of this can be found in the "Magnæ Britanniæ Notitia" by John Chamberlayne. Chamberlayne's book was written after the Act of Union to explain the new government of the then nascent Kingdom of Great Britain to two nations which previously had completely different forms of government. The book goes into great detail about which position did what prior to the Act of Union and can be found, rather conveniently, on Google Books. (Note: this is the 1737 edition, not the 1718 edition)