I have never seen it listed in SR, but does anyone here your 1" square mats to run combat scenarios with, and if so what scale do you make 1"?

I do. I make 1" = 1 meter.

It's a pain, but I go with 1.5m per square as otherwise the miniatures are too big or too small.

I should look into getting a differently sized mat as one-and-a-half inch squares would probably be close enough to "1 square = 2 meters" to work.

On the rare occasions I've done it, I've used a hex mat, and 1 hex has been anything from 1m, 2m, or 5m, depending on how large the area and how much granularity I was expecting to need.
An indoor setting where I'm expecting a brawl would definitely require higher resolution, but I've also done just fine with 5m hexes in a very large outdoor setting with a long-range firefight.
I see no particular reason why it must be consistent from map to map, as long as there's a scale.

Though I don't actually use squares or hexes in my game, I think that there is a certain elegance to having each square be 2 meters. It's a good compromise of size (allows a fairly long-range firefight to transition seemlessly to a brawl) and each hit on a Sprint test equals 1 square of movement. I've been thinking about starting to use maps for some combats (blame D&D 4E), and I think I'll likely do it that way. Though I'd likely enforce a "1-2-1" rule for diagonal moves. (First diagonal move in a turn counts as 1 square of movement, the second as 2, the third as 1 again, and so on). Free diagonal movement tends to trivialize a lot of obstacles and terrain, in my experience.

Although it has a few disadvantages over square grid, hex grid is far more useful overall, particularly for diagonal movement. A good general scale would be 1 hex = 2m, although depending on the size of the area you are mapping, you can use any of the following without to much issue - 1 hex = 1m/2m/5m/10m/20m.

I've been considering using a mat in the future. I've never used one in the past, instead opting to use blackboards and chalk to draw the terrain and the placement of the various combatants. Can someone give me the benefits to using a mat? The only one I really see is that movement and distance is exactly specified by the dimensions of the mat, but I'm not sure that such a level of specificity is really necessary.

It is portable.

I've utilized wet-erase battlemats in the past and used markers to render walls, foliage, boxes, what have you. I would scale the mat up or down (1"=1 meter to 1"=5 meters to whatever) as needed. I made Cardboard Heroes style figures for my players and my NPCs. It was handy for showing range and line of sight and keeping track of where everyone was located in an encounter. I've switched to using a projected map image on a whiteboard using a projector and a laptop loaded with Photoshop. And I made icons for each character that I move at the player's request.

Battlemaps are useful for short range and melee combat. But if you're shooting rockets, sniping from vast distances, or are engaged in aerial combat there isn't much point. It all depends on your style of play.

I prefer a hex mat (when I bother to use one) with the hexes on 2 meter centers. (You can use 5 feet centers if you like.) A "diagonal" move is much closer to 2 moves than squares. (1.73 versus 1.41)

Also works better with the d6 mechanic of SR.

As always, YMMV.

I use a battlemat with the squares for all my games. 1"=1m.

I also carry around a cheap tape measure for those times you need to calculate distance and the characters aren't in a straight line. I find it works perfectly for everything but grenade scatter, but that's a simple problem to work around.

The best setup I've seen was a ceiling mounted projector aimed down at the table. It let the game master use a computer for the maps, and terrain, while the characters and NPCs were represented by miniatures.

We used a projector for the first time last week. It was very smooth and much applauded.