Sebastian,

It depends on what kind of significance test you want to run.

If you want to run a test to see if coefficients are different form zero, sorry, that really is a t-test and that's how all logit programs I know of indicate the significance of individual parameters. It's not all that useful of a t-test because (a) the attributes in a conjoint experiment are almost always significantly different from zero and (b) because the coding used in utility estimation can itself cause attributes to have zero (or close to zero) utility - in the former case, if you use dummy coding, the reference level will necessarily be zero; in the latter case, if you use effects coding, the standard in our software, and if you have >2 levels in an attribute, very often one of them will be close to the center of the scale, and to zero: a non-significant result here doesn't mean "this attribute level has no effect," it means "because of the way the data are coded, this attribute level ended up near zero."

On the other hand, if you want to test whether your levels are different from one group of respondents to the next, then you could, if you wanted do an ANOVA (not a MANOVA) where your fixed effect is sub-group membership (assuming you have >2 subgroups - otherwise, it's still just a t-test). Of course there are better tests to run here (including the scale-adjusted logit version of the traditional Chow test) but if you like ANOVA, you can do that, too.