A question to which the answer seems obvious, never.
But not so fast. There may be times when employers do support minimum wages. As an example look at Germany. At present Germany does not have a minimum wage, but there is pressure for the introduction of one, or more correctly the introduction of a number of minimum wages. Currently in Germany collective bargaining is largely handled at the sectoral level and one idea being discussed is to adopt sectoral minimum wages, it could be that such wages would be negotiated about within the collective bargaining rounds. A question that arises is, In which sectors is support for minimum wages most likely to be found?
A new working paper looks at this question. Ronald Bachmann, Thomas Bauer and Hanna Kröger use a survey of some 800 firms in 8 different sectors and find some interesting results. Not too surprisingly I guess the support for minimum wages is greatest when they would raise barriers of entry for competitors. In effect agreeing to a minimum wage amounts to little more than the cartelisation of industry. Note that this outcome is a result of the fact that negotiations are done at the sectoral level. In such an outcome we would see a reduction in the number of firms, and most likely to a reduction in employment. However the drop in employment is not for the standard reasoning we associated with minimum wages, here the cartelisation reduces output and thus the demand for labour. You are producing less and so you need less inputs, including labour. Low productivity firms who can't afford a high minimum wage are forced out. Of course I would also expect to see higher prices and thus a reduction in welfare for consumers.
An addition question raised here is How much of this support for a minimum wage would vanish if the minimum wage setting took place at the nationwide level level rather than the sectoral level?