Of course you can sharpen a serrated blade, otherwise you couldn't make them in the first place. It is harder than sharpening a non-serrated blade but the process is similar. It does require additional tools.
You will need a set of stones or files that exactly match the profile of the blade. Usually this is a pattern made up two sizes of circular indentations, so two sets of grits plus the regular bench stones. Special cermaic stones shaped for wood carving gouges can be purchased. These are triangular in cross section and have a fine tapered edge with a rounded profile. Small rat tail round files can be used, but it can be hard to match the diameter. Sometimes you can find cheap diamond dust needle files($25 for a set of 10), the tapered round ones are ideal.
An inexpensive method is to use sheets of wet/dry sand paper folded over a stiff wire of the right diameter. Sand paper also works well as a stone for flat blades. For a 'bench stone' you can mount the sand paper to a piece of flat glass or floor tile using spray adhesive. You need to use a lubricant such as light oil or WD-40 or the paper clogs quickly. Use an assortment of grits from 600 to 2000 (finer grits are available from auto paint supply houses) See Scary sharp - Wikipedia, the free encyclopedia
for a detailed how to on using sand paper.
Most serrated blades are flat on one side. The flat side can be sharpened in the normal fashion. The serrated side needs to be sharpened one indentation at a time. Run the abrasive tool through each scallop, cut in one direction, not back and forth (clogs up quickly if you do) Take special care to match the existing bevel angle. It helps to mount the blade in a vise of some kind.
Start on the serrated side, working from course grit to fine. From time to time flip the blade over and run the flat of the blade over a stone to take of the 'feather'. Similar to sharpening a chisel. Use only fine grits on the flat side, it takes for ever to restore a smooth finish if you use course.
Note: pay special attention to the bevel, if any on the flat side. Often the flat side of the blade has no edge bevel, in this case the blade is only sharpened on the serrated side and only flattened on the back side. For an aggresive cutting edge (like rope) take one final pass though each of the scallops a coarse grit stone. This leaves tiny scratches that act as micro serrations in the edge.