How to make smooth slow motion from normal footage
Slow a clip in Video by Zaweba and set its in-between frames to optical flow, which warps and mixes neighbouring frames for smooth slow motion.

Smooth slow motion from ordinary footage comes down to how the missing frames are made. In Video by Zaweba, slow the clip down, then set its in-betweens to optical flow, which matches blocks of pixels between neighbouring frames and warps and mixes them to create new frames in between. The result plays smoothly instead of stuttering, both in the preview and in the export.
Footage filmed at a normal frame rate only has so many pictures in each second. Slow it to half speed and you need twice as many. Something has to fill the gaps, and the choice of what fills them is the whole difference between juddery and smooth.
Three ways to fill the gaps
Each clip in Video by Zaweba has a setting for how in-between frames are made. Repeat frames simply shows each original frame twice, or more, which looks like a stuttering step motion. Blend frames mixes two neighbouring frames together, which is smoother but can look ghostly, with faint double images on moving things. Optical flow works out where each block of pixels moved from one frame to the next and draws a new frame partway along that movement.
Optical flow is the one for smooth slow motion. Repeat frames is still useful as a deliberate stylised look, and blend frames can work well on slow, soft movement where flow has little to gain.
Slowing the clip down
Change the clip's speed in the usual way. Plain speed changes run from 0.25 to 4 times, and the sound keeps its pitch, so a slowed clip doesn't drop to a growl. For a slow motion moment inside a clip that otherwise plays at normal speed, use a speed ramp instead: Inspector > Speed and time > Ramp the speed keyframes the speed so it can ease down and back up.
Then set the clip's in-betweens to optical flow. The preview uses it too, so you can judge the result straight away rather than waiting for an export.
Choosing footage that slows well
Optical flow guesses, and some shots are easier to guess than others. It does best with clear, steady movement against a stable background: a runner crossing the frame, a bird in flight against sky, water pouring. It struggles where things cross in front of each other, with very fast spinning objects, and with fine detail like hair or leaves in wind, where it may leave smeared or wobbly patches.
Shutter speed matters as well. Footage shot with a lot of motion blur keeps that blur when slowed, so even perfect in-between frames look soft. Sharp frames give flow more to work with.
How far to push it
Half speed is usually safe. Quarter speed is possible but asks flow to invent three new frames for every real one, so artefacts become easier to spot. Watch the edges of moving objects at full size, since that's where trouble shows first. If a patch goes strange, trim the slow section to avoid it, or switch that clip to blend frames and see which looks less wrong.
Finishing the shot
Slow motion feels best with sound that suits it. Lower or mute the original sound and let music carry the moment, or use the sound mixer to bring in an ambient bed. A gentle colour grade and a cut on the action into and out of the slow section help it feel deliberate.
When you export, the same optical flow frames are rendered as you saw them, so what played smoothly in the preview stays smooth in the file.