Well, if they have missiles and you don't have point defense you have a tough road. Best bet is to do what motlee, sj and Q suggest and blockade them into surrender.
And research Point defense soon, you will need it!
I just thought of something... Try using "planetary weapons" tech. The first few levels are dirt cheap, and the planetary napalm will do a lot of damage. Try a bunch of ships with napalm to convince the enemy to surrender.
BTW, are you sure that that is their Last planet? They may have started growing somewhere else without your knowledge.