There are couple of very well known zoom lenses with macro capabilities. By macro I don't mean the garden variety 1:4 ratio that pretty much every zoom lens possesses. The Nikon Micro-Nikkor 70-180mm is probably the most popular, but expensive macro zoom, that can focus to 1:1.33 ratio at 180mm. The Vivitar Series-1 90-180mm f4.5 Flat Field Macro Zoom is a cult-classic that can do 1:2 half life size at 180mm. These two lenses were designed with macro capabilities in mind and thus the image quality in macro mode is much better than other zooms with macro features as an afterthought. One lesser known lens, the Tamron SP 60-300mm f3.8-5.4, has very capable macro mode, and deserving of a look if you are looking for a zoom lens with macro capabilities. This lens has a maximum magnification ratio of 1:1.55 at 60mm, but majority of owners of this lens, if they do not read the instruction manual, would not know how to access this macro feature.
To activate this macro mode, you need to collapse the lens to 60mm, then focus the lens to minimum focus distance of 1.9m, and when you hear the focusing ring stop, apply more force and continue to turn the focusing ring until the yellow macro line on the focusing ring is aligned with the macro line on the lens barrel. The special macro mode is now engaged. If you slide the zoom ring outward, it will reveal the 1:1.55 mark that's normally hidden. The biggest negative of this mode? The focusing ring is locked and you can not use it to focus. You can only move back and forth to focus. It awkward and unnatural to use than a true macro lens, but if you don't want to spend the money to buy a true macro lens, this lens can be used in a pinch.
Aside from its macro capabilities, the Tamron SP 60-300mm lens has a very versatile zoom range. Many people dismiss this lens because it's not very sharp wide open, especially the corners and edges, but at f8-f11, it is very acceptable across the frame. True, it lacks micro contrast the gives the pictures "bite", compared to a prime, but the 5x zoom range is more than makes up for it, and the macro capability is definitely a nice bonus. I am not a zoom lover, but I like this lens a lot. The only downside, is the weight and size. The lens itself is not very large in diameter with a 62mm filter size, but it's very dense and long, weighing more than 2 lbs. One of the biggest advantage of this lens against the Nikon's micro Nikkor and the Vivitar, is the price. It's often sold for around $60USD or less, compared to around $1000 for the Nikon, and around $150-$300 for the Vivitar.
All pictures below were taken with Tamron SP 60-300mm f3.8-5.4 & Sony A7