If you have a ground plane, then the guard ring will have little impact.
Guard rings are usually to protect high impedance inputs like specialized op-amps, not so much for EMI radiation.
National Semiconductor Application Note 241
ELECTRICAL GUARDING
The effects of board leakage can be minimized using an old trick known as guarding. Here the input circuitry is
surrounded by a conductive trace that is connected to a low impedance
point at the same potential as the inputs. The electrical connection
of the guard for the basic op amp configurations is shown in Figure 5.
The guard absorbs the leakage from other points on the board,
drastically reducing that reaching the input circuitry. To be
completely effective, there should be a guard ring on both sides of
the printed-circuit board. It is still recommended for single-sided
boards, but what happens on the unguarded side is difficult to analyze
unless Teflon inserts are used on the input leads. Further, although
surface leakage can be virtually eliminated, the reduction in bulk
leakage is much less. The reduction in bulk leakage for double-sided
guarding is about an order of magnitude, but this depends on board
thickness and the width of the guard ring. If there are bulk leakage
problems, Teflon inserts on the through holes and Teflon or kel-F
standoffs for terminations can be used. These two materials have
excellent surface properties without surface treatment even in
high-humidity environments.

In fact, if you have the guard ring close to a high current node, it can pick up that noise and radiate it like an antenna.
Again, for best EMI performance, a good solid ground plane, with lots of ground via connections is best. eg. Don't use a single 20mil via when you can use two or three 10 mill vias.