Two examples of artifacts that were mobile, used in battle and had dramatic effects:
The battle of the standard used a cart with consecrated banners, and is credited with influencing the military victory.
The Danish flag fell from heaven to aid Waldemar the great in his hour of need, and as Denmark has used the white cross on a red background since it apparently sets the record for national flag in longest continual use.
But either not yet relics when in battle (the dannebrog) or not used in battle against pagans (the "standard").
The most famous medieval relic flag is the Oriflamme - by its 11th century legend (Chanson de Roland) the flag carried by Charlemagne in an a-historical crusade.
A relic Oriflamme was used in battle already by Louis VI, at Bouvines 1214 by Philippe II Auguste and still at Agincourt - but never in battles or missions among the pagans. It was the flag of the French king, after all.
Reading Georges Duby's Le dimanche de Bouvines (1973 Gallimard, translated in many languages), you see how its presence in that battle for the chronicles stressed its sacred aspect.
Two very precious portable altars with lots of relics in them are the Hildesheim Portable Altar and the Portable Altar of Countess Gertrude.
They are described in detail - analyzing all their contained relics - in:
Matter of Faith:
An Interdisciplinary
Study of Relics and
Relic Veneration
in the Medieval Period
(2014 British Museum, for free here).
Such portable altars of course were no altars for missionary work among the pagans.
Often said to be a 'Gift From God' though 
From around 16th century on.
Petrus Olai freely uses Exodus 17:8-16 to describe the battle where the dannebrog fell from the sky, and may be further inspired by legends around the Battle of the Milvian Bridge:
The flag itself is older than the legend: see the late 14th century Gelre Armorial.