Siege Campaigns are hard, not gonna lie to you. But nonetheless, they are fun to play and fun to see how the leadership of the PC's come out. Here are some of the trouble areas:
1: Time consuming. Sieges are long, long battles, that usually end when either the city runs out of food to sustain, the attacking party dies off, or anything in the middle. Keep in mind this won't be a one or two day thing. Make sure your PC's know that they are gonna be in for the long haul and plan accordingly. Food supplies can run short, diseases can take the city, fires break out. There's a whole gambit of problem that can happen
2: A lot goes on. sieges have quite a few elements that can get confusing as far as spacing out time frames. Not only is there the simple aspect of the attacking army, but there is the problem of thieves, murderers, smugglers, traitors, spies etc. As a DM, keep your mind open to the different things that happen during a siege. Watch movies, they'll give you plenty of ideas.
3: Command/leadership. its common that one player may have a better grasp on what the other may have. In that case, it may be better to have people lead separate groups or be responsible for separate areas of the kingdom. (political leader, head of the guard, head of defenses etc.)
Most of all, have fun with it. Its good to see how a good team can come together when defending a city.
Think of the individual crises as Encounters. Plan on the players sallying out to raid the besiegers. Is their city on the coast? Use water encounters =). Sappers, or sewer raiders? Did the invasion capture any sections of the city? The party can fight to get them back =).
GNOME