I believe it will end up being a lot like that described in Niven's "Protector"... you launch your weapons, and, five years later, you look to see if they hit.
That's for interstellar combat. For orbital combat... a lot would depend on the goal. Are you trying to knock out the enemy's satellites? Drop bombs on his population centers? Stop his transport ships from leaving Earth and getting to their destinations?
The easy answer is "drones, drones, and more drones", but this assumes ECCM will equal ECM well enough to make it at least a tossup that you'll get through the other guy's defenses. I'd also make a guess that we'll never get as much damage potential out of a beam weapon as we will out of an explosive, and the simpler the technology, the less things can go wrong. I'm seeing, basically, drones that get as far as they can from the enemy, analyze their motions, and then launch direct-fire weapons based on prediction algorithms as to where the enemy will be when the projectiles get there. I'd also speculate that anything launched, including the drones, would be absolutely blind to any kind of orders to go home, change targets, respond to IFF, etc, because the chances of being fed false data are too great. This would lead, of course, to the launch of basically uncontrolled weapons armed with considerable destructive power, so, if they were hacked pre-launch... oops...
This, in turn, might lead to remote control, where the drones have no "brains" but are piloted by humans. Of course, this opens the same problem -- if the drones are controlled in any way by an outside signal, an enemy can and will find a way to hijack that signal. So, back to self-guided vehicles with no way to turn them off or shut them down. (And even this leads to problems... if there's a "mission complete, go home" algorithm, you run the risk of someone figuring out what the drone needs to "see" to conclude "mission complete" and finding a way to fake it. So, logically, you just have the drone explode when it's done.
If the general area being fought over is well defined, you might have some kind of minefield, using virtually-inert devices that rely on passive sensors to come to life and go 'boom' when something is near, but I've read a lot of people arguing that nothing is inert enough to not be trivially detected far off.
(Of course, I'm not sure there's anything to fight over in space other than to knock out the other guy's satellites, and there won't be anything else up there for a long, long time... so long that making predictions about the kind of tech used is probably impossible. As for the satellites, it's probably much easier to just fire some ground-based or plane-based missiles at them than to try for any kind of "space war".)