I wish to change my Canon G15 camera for an M2 or M3 (when available) mirrorless one. With G15 it is rather easy to shoot macro photos — this is included in the features of the camera and lens. Will it be as easy also with a standard lens (55mm or 18-55 zoom) on M2 or M3?
No. It will be harder. The larger sensor in the EOS M2/M3 is the same size as one in a Canon APS-C dSLR. The larger sensor size requires larger (longer) lenses, and this in turn makes for a thinner depth of field and a larger minimum focus distance.
In addition to this, the M2 and M3 are only sold in Asian/European markets, and the EOS M lens lineup does not yet include a macro lens of any kind. In addition, both the ultrawide zoom and the telephoto zoom are only sold in Asian markets. If you are in the US, the only two native mount lenses you can purchase are the 18-55 kit, and the 22mm f/2 STM prime--there is no 55mm prime for the system.
This would be the same with nearly every mirrorless camera system--the sensors are typically much larger than those in P&S cameras, and are closer to the sensor sizes found in dSLRs (Pentax Q excepted). If this close-up capability without a specialized macro lens is important to you, you may have to limit the sensor size of the cameras you're willing to look at. Perhaps consider 1"-format sensored cameras, like the Nikon 1 mirrorless system, or the fixed-lens Canon Powershot G7 X or Sony RX-100 models.