Click here for a paper on hanging your shield
Under current Ansteorran rules, shields of any size up 450 square inches and of almost any shape can be used against any rapier blade (yes, that includes epees and foils). Why 450 square inches? Because that is about the surface area of a 24" diameter circle. Here are a few other restrictions:
No single dimension can be over 4 feet. Thus you cannot use a rectangle 6 feet long and 9 inches wide.
No sharp corners, points or protrusions are allowed
Do not select a shape that is likely to trap blades. In general, avoid shapes with holes or slots.
The final product must be light weight, thus most heavy weapons shields are not legal for rapier.
I find that shields of about 250 square inches (18 inch diameter)
and less handle very differently than shields that are larger than
that. In fact, they handle so differently that I consider them
different styles, just as rapiers are different from daggers. The
smaller shields  called bucklers  are a very active defense as it
is necessary to move the buckler around a lot to cover targets and
make openings. The larger shields  called targets  usually strap
to the arm and form a much more static defense, moving less than
their smaller cousins because they naturally cover more area.
It is easy to make a round shield, but is that really the best choice? Many shapes were common in the 16^{th} and 17^{th} centuries so there are a lot from which to choose and still remain historically accurate. While it is certainly possible to master the round shield, the novice  and even most experienced fighters  will find they have great weaknesses. Other shapes have a more immediately strong defense. As one knight explained it to me:
"The corners on a shield protect you and so they are your friends. A round shield has no corners, so round shields are nobody's friends."
Overstated a bit, perhaps, but it does make the point. Particularly with targets, a shape that has corners at the top of your shield makes it much easier to defend with that shield.
I think one of the main reasons people often go with the round shape is that the math for figuring the surface area is already done for you. Still, none of the math is particularly hard. For example, if you wanted to make a rectangle of 450 sq. in. just pick how wide you want to make the shield and then divide 450 by that number to see how tall you are allowed to make the shield. Adjust until you find the best combination for you. Some sizes that work are : [18 wide x 25 tall], [15 wide x 30 tall], [20 wide x 22.5 tall] and [21wide x 21 tall]. The formula for some basic shapes can be found at the bottom of this page.
So, what if you want a more complex shape, or you are a marshal and must measure a shield of questionable size? Most shapes are similar to simple shapes or they can be easily broken down into simple shapes. For example, consider how the shapes below are very similar to a rectangle and a circle:


See how this heater shape can be easily represented by a rectangle on top of a triangle. Even a complex shape like a six pointed star is similar to six triangles and a circle:


Don't worry about being too exact. If you are building the shield, build it a little smaller to be on the safe side. If you are a marshal, be generous in your assessment. Disallow the shields that are OBVIOUSLY too big.
For the heater shape above, a good size under 450 sq. in. would be to make the rectangle 20 wide x 12 tall and the triangle 22.5 at the base x 18 inches tall. Notice that the base of the triangle is wider than the rectangle. That is because it must be wider to encompass the curves at the bottom of the heater shape. Also notice, that makes for a shield a little under 30 inches tall.
[In late breaking news, I have worked out another shape I think
will work well in melee. It is basically a 17" wide x 12" high
rectangle on top of a triangle that is 17" at the base and 28"
tall, with the last couple inches of the tip cut off. This shape
should help protect the leg, especially if you lead with your
sword side leg like most fencers. However, if you are big, 17"
may not cover you.]
Formula for the surface area of a circle: 
Formula for the surface area of a
rectangle: 
Formula for the surface area of an isosceles
triangle or a right triangle: 