Do what they have in every other case of split up in the former Yugoslavia; have the Serbian majority areas try to secede from the new state. There is a corner of Kosovo in the northeast that is contiguous with the rest of Serbia.
In addition, they can try an economic boycott of Kosovo, refusing to provide power or other key economic goods.
Thirdly, they will downgrade diplomatic ties with each state that recognizes Kosovo.
There are other strategies that are more chancy: calling on Russian forces to protect their remaining corner of Kosovo. This is chancy because now Serbia is landlocked, and neighboring states could deny Russia overflight and ground routes to supply their army. I don’t know if Vladimir Vladmirovich wants to do the “Pristina Airlift” if he can’t get permission from Hungary or Croatia to reach Belgrade.
There are small forces in both Serbia and Kosovo who want to provoke a shooting war. I think the SFOR would squash that.
This is a bad business all around. There could have been diplomatic solutions reaching all the way back to February 1999 in Rambouillet, but one side or another — usually the Serbs, because they felt they had the most to lose — refused to compromise.
Russia is in a very good position to deal with European supporters of Kosovo independence. They have only to shut off their natural gas pipeline to Europe, and Putin is looking for an excuse for a showdown.