The universality of the continuum limit and the applicability of renor
malized perturbation theory are tested in the SU(2) lattice gauge theo
ry by computing two different non-perturbatively defined running coupl
ings over a large range of energies. The lattice data (which were gene
rated on the powerful APE computers at Rome II and DESY) are extrapola
ted to the continuum limit by simulating sequences of lattices with de
creasing spacings, Our results confirm the expected universality at al
l energies to a precision of a few percent, We find, however, that per
turbation theory must be used with care when matching different renorm
alized couplings at high energies.