A commenter asked what happened to the relic of St Andrews that were brought to St Andrews by St Regulus. The short answer is "We just don't know." It is very likely that they were destroyed in the wake of Knox's sermons. He was fiercely opposed to the veneration of relics and it is unlikely that the mob would have respected them any more than the artwork of the Cathedral.
However, there are other relics of St Andrew, notably at Amalfi where they were taken after being taken from Constantinople in the 13th century. Pope Paul VI returned a part of the relics to Patras in 1964 as an ecumenical gesture of goodwill. The Wikipedia article on St Andrew has further useful information about various traditions relating to the saint.
In 1879, the Archbishop of Amalfi sent a piece of the saint's shoulder blade to the newly re-established Catholic community in Scotland. In 1969, when Gordon Gray was in Rome to be appointed the first Scots Cardinal since the Reformation, Pope Paul VI gave him some more relics of the saint with the words "St Peter gives you his brother." These relics are now kept in a reliquary in St Mary's Cathedral in Edinburgh.