The Kingdom of Jerusalem already had two very famous relics when the Second Crusade arrived in the East. These were a piece of the True Cross and the Holy Lance. The provenance of both are questionable but their value lay in their figurative importance.

The Holy Lance was the instrument used to stab Jesus Christ in the side while he was on the cross. The example in question was re-discovered in 1098 during the capture of Antioch. A Frenchman named Peter Bartholomew told of visions he had experienced, suggesting that the Lance was buried in the Church of St. Peter. After a night of digging, Peter went down personally into the pit and produced the Lance. At the time opinion was seriously divided on whether this find could be accepted as genuine, but the crusaders were besieged and morale was low. Raymond of Toulouse seemingly believed Peter and word spread throughout the city of the blessing which had been bestowed on the army. The crusaders, their belief somewhat renewed, subsequently broke the siege and the campaign survived.

The True Cross was reclaimed a year later in 1099. It had supposedly been hidden for almost a century in Jerusalem by Greek priests, before the new Latin Patriarch Arnulf seized it from them and gave it pride of place in the Church of the Holy Sepulcher. Subsequently, the Patriarch would carry the Cross before the army of Jerusalem before battle. It was in this way lost to Saladin at the Battle of Hattin in 1187. Richard the Lionheart attempted to ransom it back in 1191, but it had been lost or destroyed.

Keep in mind that the proliferation of, and trade in, relics was vast in this period. Practically every institution had a finger of someone or a fragment of something. What was actually important was the faith and reverence which the item could command, not its solid basis in historical fact. For this reason, items like the Patriarch's Cross were of considerable significance.

The unlike the First and Third Crusades, the Second Crusade didn't actually capture anything of strategic importance in the East, so the potential for capturing relics wasn't present.

I've tried to be as concise as I can, the Crusades are fascinating but also huge in their scope, I hope the information above is of use to you and helps you explore further. For a good grounding in the subject try:

God's War by Tyerman - a really detailed single volume.

History of the Crusades by Runciman - the narrative classic on the period, in three volumes.

Edit: Typing while tired.