When I've printed an object I've had to choose between high resolution and quick prints. What techniques or technologies can I use or deploy to speed up my high resolution prints?
You could experiment with slicing. For example, you might not need high resolution all over the object, but you can speed up some straight parts by using greater layer high there. See a part of Slic3r manual about such thing.
It is also possible to print thicker infill every Nth layer, see Infill optimization in Slic3r.
Other slicers might have those features as well.
For FDM technologies in general with a single extruder, slicing modifications is your only options. However there will be a trade off between quality and speed. For ABS, changing to a machine with a enclosed build (such as a zortrax) chamber may help and a heated build chamber (Stratasys machine) will help the quality and reliability but not the print speed directly. As ABS has a tendency to warp vase mode is not the best idea either.
If you only need high resolution and not strength then reducing the infill percentage or even using vase mode will speed up the print. Also changing to a material that you can print at higher speeds like PLA will magnify any of the previous settings.
If you have two extruders then changing to a wider nozzle and using that for infill may speed up the print, heating and cooling time during extruder changeover may actually make it slower.
For other technologies there are lots of options digital light projection (DLP) and stereolithography (SLA) both provide significantly higher resolution then FDM, with DLP being the faster of the two, comparison. Take the review with a grain of salt though as the technologies are far from standardised, for example out DLP at work offers far higher resolution and speed then our SLA which is quite old.
Sintering or melting technologies can scan the outline every layer then perform a infill of multiple layers at once to speed up the process.