Side note: Actually fighting involves very little parrying, because weapons lose their edge and break much easier then you would expect. The only weapon I can think of that is meant to be consistently used to block a blow is the rapier, and that works because it has no edge and is very flexible.
When the wielder only has a sword theres much parrying. Any 'blocking' would be deflective rather than trying to stop the attack unless one has a heavier kind of sword and it is never edge to edge.
Take the twohander(zweihander). In a german sword style it has a basic defensive posture where you hold the sword upside down at your side with the cross guard at shoulder height that basically covers your whole body. This pose lets you make a quick leg strike, sideway swing and a powerful strike from above.
Many swords, from longswords(varies) and larger have a part of the blade by the hilt that is not edged and thus slightly thicker. I assume we're not talking about crappy swords, but this zone is rather sturdy.
Most blocking occurs by stepping in and stopping the opponents strike before it's in full swing so there's not that much force to damage the blade. At other times you either dodge or deflect the strike with the side of the sword.
There's both dual edged rapiers and the rounded piercing one and this is a very light weapon so it would only be used to block another rapier, but it can probably deflect a strike.
Has for the so claiment "edge", on very big swords it doens't matter anyway, the blow it mainly concussive anyway, relying more of speed/mass to chop people. Kinda like woodaxes, they aren't "sharp", but still cut because they have a lot of force.
True, but one would still keep a sharp edge to be able to slice when needed. except for that scottish or irish one that was just simply huge, forgot the name.