We demonstrate a trap that confines polarizable particles around the antinode of a standing-wave microwave field. The trap relies only on the polarizability of the particles far from any resonances, so can trap a wide variety of atoms and molecules in a wide range of internal states, including the ground state. The trap has a volume of about 10 cm 3 , and a depth approaching 1 K for many polar molecules. We measure the trap properties using 7 Li atoms, showing that when the input microwave power is 610 W, the atoms remain trapped with a 1/e lifetime of 1.76(12) s, oscillating with an axial frequency of 28.55(5) Hz and a radial frequency of 8.81(8) Hz. The trap is particularly well suited to sympathetic cooling and evaporative cooling of molecules.