You can project the shape to a new coordinate system and retrieve the new min/max x,y values using the following example...
Dim g1 As IGeometry
Dim pSR As ISpatialReference
Dim pSREnv As New SpatialReferenceEnvironment
'pick an appropriate Spatial reference here
pSR = pSREnv.CreateProjectedCoordinateSystem(esriSRProjCSType.esriSRProjCS_NAD1983)
'project the envelope you already have to the enw spatial reference
g1.Project(pSR)
'Now you your values from g1
Regards,
Anna