What motherboard do you have? Chances are its a BX board so therefore the new processor would have to have a 100Mhz FSB.
I did that upgrade a few months back with a Supermicro P6SBA and Pentium III 350 - I got hold of a slocket adaptor and a 850 Pentium III, 100Mhz FSB - worked perfectly although you do need to flash your BIOS in most instances.