It's true, Necrons lack a close combat monster unit, a true Deathstar. You won't find any TH/SS, Nob Bikers or Paladins here. Sure, Lychguards can be very expensive but could they go toe to toe with any of the aforementioned units? You can do the maths for me, be my guest.
However, there is a unit in the codex that doesn't have all the crippling weaknesses the other Necron close combat units have. The Wraiths! They might not be as powerful as some units from other books but they can still be quite effective. Let's make them into a Deathstar, shall we?
Destroyer Lord, Mindshackle Scarabs 
6 Canoptek Wraiths, 4 Whip Coils, 2 Particle Caster 
For 405 we have a fairly good close combat unit that could beat some face. It's is fairly mobile to start with and we don't need to buy a vehicle for them (very big plus). They don't count as jetbikes any more unfortunately but thanks to their special rules they can go from cover to cover without suffering any delays or harm. A possible second turn charge in most cases.
They are quite survivable too. The unit has 4 different equipment groups (one Wraith will have a Particle Caster and a Whip Coil) so they will soak up a few wounds before one of them dies. The Lord will always get a double strength hits from shooting allocated to him and 3++ for the rest of them is pretty neat.
Most importantly, they don't suffer from that I2 that all other Necrons do. Well, they do actually but Whip Coils will mend that. They have 24 attacks on the charge so we should be looking for 10 wounds before saves (2 of them rending) against MEQ units and another 2-3 power weapon wounds from the Destoyer Lord. The latter is not a close combat monster like some characters from other codices (especially that WS4 really hurts) but with rerolls to hit and S7 he can do some damage.
Don't forget the Mindshackle Scarabs either. Always charge the Lord on the model with the special close combat weapon in the opposing squad or a killy IC. Failing a Ld 9 check on 3 dice is done very easily. A Space Marine Sergeant hitting his own men with a powerfist must be a very comical sight (and up to 3 hits can be nasty). I wonder how it works against single model units (ie Monstrous Creatures).That's not just an offensive ability though. It will help your Lord stay alive too. Make sure he only makes contact with that model and in most cases nothing will hit him back.
This unit can also be very effective against vehicles as well. A good number of attacks plus high strength and Rending/Warscythe will do the work. Especially if you have managed to immobilised the vehicle with your Gauss Weapons, the Wraithstar will make short work of even a Land Raider.
In conclusion, the Wraithstar unit is quite mobile, very high on the survivability scale and will do enough damage against all units including vehicles and it's not too expensive. What's not to like?