i put something delicious inside a lunchbag size paper bag, & lay it on it's side, open. critter goes in, and i scoop up the bag and carry it outside... for larger critters a wastepaper basket works too.
of course this is labor intensive cause you have to hover; out of the immediate area where the bag is, but close enough to see it and grab it up right away. but i've used this method successfully when kitty brings critters in the house, i praise her for her grand hunting abilities,
then i catch critter and let him out. sometimes we 'hunt' together... she'll find the area where it's hiding, paw at it and howl, and i move the furniture to get at it. fun!