So far I've used a squadron of seven
Sussex-class frigates for anti-missile duties. They're rather old by now, however, and due to be replaced with a more advanced successor in the near future.
Sussex class Frigate 7,800 tons 616 Crew 2244.5 BP TCS 156 TH 500 EM 600
6410 km/s Armour 4-35 Shields 20-300 Sensors 36/36/0/0 Damage Control Rating 5 PPV 64
Annual Failure Rate: 97% IFR: 1.4% Maint Capacity 899 MSP Max Repair 216 MSP Est Time: 2.43 Years
GN-125M5 APOLLO MagCon Fusion Drive ( 8 ) Power 125 Fuel Use 50% Signature 62.5 Armour 0 Exp 5%
Fuel Capacity 150,000 Litres Range 69.2 billion km (125 days at full power)
GenCore Theta-class R300/20 Barriers (5) Total Fuel Cost 100 Litres per day
Rheinmetall R3 Quad Gauss Turret (2x12) Range 30,000km TS: 16000 km/s Power 0-0 RM 3 ROF 5 1 1 1 0 0 0 0 0 0 0
Fire Control S06 90-16000 (2) Max Range: 180,000 km TS: 16000 km/s 94 89 83 78 72 67 61 56 50 44
Sentinel 3R19 Missile Defence LADAR (1) GPS 108 Range 19.4m km Resolution 1
Artemis ALS 86-20 (1) GPS 2160 Range 86.9m km Resolution 20
Hunter PST 2.36 (1) Sensitivity 36 Detect Sig Strength 1000: 36m km
Hunter PSE 2.36 (1) Sensitivity 36 Detect Sig Strength 1000: 36m km
ECM 40
This design is classed as a Military Vessel for maintenance purposes
You don't
need to keep up with their missile speed. Yes, turrets can get big, but put them on dedicated escorts like that and you're golden. 40k-ish km/s seems to be a common speed for Precursor anti-ship missiles, and with 16k km/s tracking (which means 4000 km/s beam fire control tech: not advanced at all), you have an easily achievable maximum accuracy of 40%. Per shot.
Each barrel would fire 4-5 shots (I think mine fired 3, though). Quadruple turrets therefore spit out four times that. So you end up firing, in my modest case, 12 shots per turret. 24 per frigate. 168 total shots in my squadron's case. 168 40% chances. An average of 67 missiles destroyed every five seconds. Forever.
I think one turret can only engage one salvo at a time, but with 14 platforms in my case, it'd be hard to be outnumbered in this regard.
The only time my point-defense bubble was overwhelmed was one time a Precursor
AMM PDC engaged my battle group with a considerable number of 60-missile salvos. They were tiny, warhead 1 missiles, but flew at close to 70k km/s (68,700 km/s, I believe). I don't quite remember, but I think at least 15% of every salvo got through, but thankfully didn't cause much damage.
Sure, if those had been larger warheads, I would've been in a pickle. But so far I haven't encountered enemies with such capabilities. But even if I do, the new turrets (and associated FC modules) I've designed have a tracking speed of 32k km/s, and fire 5 shots instead of 3 every five seconds. Not only would they have better accuracy (45%) against hypothetical 70k km/s anti-ship missiles than the old turrets did against 40k km/s ones, but also fire 67% faster, meaning 67% more chances to score hits.
That said, and playing my own devil's advocate, considering you can fit around 20 size-1 AMMs in a single HS (depending on magazine technology), you could potentially have all the AMMs you'll ever need for a single engagment (launchers included) in the space a pair of quad Gauss turrets would otherwise take. With better range and maybe even better accuracy. This would come at the expense of limited ammo and more logistics considerations, of course, but that may or may not be a problem.
I wouldn't mind if it worked like that, because that would mean we have at least two perfectly valid alternatives for anti-missile defense. And multiple balanced options is what makes Aurora grand.
PS: Yes, a layered defense is also possible, but it's a logistics hassle and I've yet to find a threat that warrants the use of such a setup. And besides, such strategy implies compromising each method for the sake of the other, raising the question of whether fully focusing on a single option would've been just as effective. If not more.
EDIT: De-smilified my design.