What happens if there is no relic in a summoning? In Unlimited Blade Works, we eventually learn that Archer was summoned as Rin had a relic associated with him (i.e. the pendant Shiro keeps). In the recent anime adaptation, there is also some statement to the effect of "a relic is required to summon a servant".

Similar sentiment is expressed in the Fate route of the visual novel. On the last day, Saber tells Shiro that he must have been able to summon her as a result of having had Excalibur's sheath embedded in him (similar to how it was embedded in Irisviel in Fate/Zero):


  To summon a heroic spirit, one needs a symbol connected with that spirit.


This seems in line with the other summonings we see, such as Waver's use of a cloak to summon Iskandar and the trouble the Einsberns take to retrieve the sheath so that Kiritsugu summons a good servant. Finally, some remark Lord El Melloi makes about having to find a relic last minute suggests that a relic is always required.

Is this ("a relic is always required for a successful summoning") correct? If so, did Rin have anything she knew to be a relic when she summoned Archer? (I feel like she didn't, but if a relic is required, I would have assumed that she'd be aware of this, as a reasonably competent magus.)
A catalyst is not required, but most Magi prepare for one because they have been preparing to partake in the Holy Grail War for years.


  Most Masters will prepare a catalyst with which to summon their desired Heroic Spirit, but it is not absolutely necessary. Without a specific artifact, the Grail will, rather than base it on their power, chose a Servant based upon similarities to the summoner's own nature.


Source: Servant - Summoning

This coincides with Gilles de Rais' summoning in the 4th Holy Grail War:


  His Master was Ryuunosuke Uryuu, a serial killer who unwittingly performed a successful summoning ritual using the blood of a murdered family. Ryuunosuke lacked a cataylst so the Grail chose a servant with the closest personality to Ryuunosuke. He first introduces himself to his Master as Bluebeard.


Source: Caster (Fate/Zero) - Role

You can see a list of all the the heroes who are known to have been summoned with a catalyst in the Catalyst section of the Servant page, and you'll notice that not only Gilles is missing.

You'll also notice that the mirror used to summon Medusa was a weak catalyst, so Sakura's similar personality helped summoning Medusa:


  Mirror dug up from a temple in Eritrea, an item with ties to an old Earth goddess of Greece. It is noted to have been a weak catalyst to Medusa, so Sakura Matou's similar personality plays a role in the summoning.