We could fight the siege out on the tabletop. I wrote the siege rules in Age of Reason, and have done quite a few tabletop sieges. It's way different than an open field fight. A field battle is kind of fluid. There's movement, and things ebb and flow. In a siege, everything feels static. But there's a certain inevitability. But, let's assume that we don't have a table to dedicate to this, or the miniature fortress.
A siege is really an exercise in supply. By the 18th Century a siege was more or less semi-predictable. As a rule of thumb, seven weeks after the opening of trenches, the defenders should be in a position to surrender. Now this assumes a whole lot of things go right with the supply. But in 1708 a lot of the campaign focused around prosecuting or defending the siege of Lille. In fact, if one wants a mini-campaign, that is the perfect excuse.
So, the attacker has to establish a valid depot on the city. That represents the siege works. Every turn that the depot is in supply, the attacker throws 1d6 and subtracts that number from the siege value of the fortress. When the siege value is zero or less, the fortress surrenders.
Now when making this die throw, every time a six is thrown, the attacker loses a strength point. If there is a garrison other than the "automatic" one (i.e. field troops sheltering in the fortress) they move to the nearest unbesieged friendly fortress. If there aren't any, they become prisoners of war to be exchanged later.
For those who thinks this means sieges will be too short, an average fortress siege strength of 14 should be sufficient.
What of the defender? What recourse do they have? They can try to break the supply line, which keeps the siege die throw from happening.
Extra about Supply
All troops outside of a fortress lose three strength points every turn starting on the November 1st turn. So a force that is 20 strength points on the December 15th turn, will be on their third turn of attrition. Readers will note that the average depot will suddenly go ungarrisoned due to attrition, putting all sorts of people out of supply. The lesson here is to go into winter quarters in a fortress.
Troops who are in a fortress on the November 1st turn are automatically considered in Winter Quarters, and cannot come out of them.
So now we can move the troops, and feed them. We've also given a reason for the campaigns. So now we will turn our attention to such things as recon, and things like that. Then we will have to deal with the diplomatic situation, and the early stages as the armies mobilize and gear up for war.