For maps focusing on a region of interest, but including surrounding areas to provide a setting, new azimuthal projections have been developed with a 'magnifying-glass' effect. On two such projections, inside a circle bounding the region of interest is a standard Azimuthal Equidistant or Lambert Azimuthal Equal-Area projection. Between this circle and an outer bounding circle azimuths remain true and the radial or area scale, respectively, remains constant, but at a reduced value. On four other projections, the inner portion is a standard azimuthal projection, which may be Stereographic, Gnomonic, or the above, but beyond this portion, the radial scale is gradually reduced to zero. Equivalents with rectangular boundaries are also available.