There are three problems when it comes to mutes:
1) many have little effect on the volume of the instrument,
2) some can cause an unpleasant vibration (which can be rather penetrating thus defeating the point),
3) some won't fit properly over a bridge (particularly on a cello).
I have tried a selection of mutes for cello, violin and viola.
Those little round rubber ones make hardly any difference to the volume on even a small instrument.
Heavier rubber ones have more of a muting effect without altering the tone of the instrument much. Their muting is still rather limited though.
Small metal ones seem to give mediocre muting with an unpleasant vibration.
The heavier metal ones covered with rubber seem to be the most effective especially on larger instruments, but can be too muting on a smaller one and give a thin whining tone. These tend to fit over the length of the bridge.
The best I have found for a cello and viola so far on ebay has been by ARTINO (in the USA). They gave significant muting of the cello and even subdued my viola. The tone of each still sounded fine.
For the violin I use a heavy rubber 'ultra' mute. Not as muting as the Artino, but better than the small rubber/metal ones. It gave a good level of muting without destroying the tone.
I have yet to find a mute that works well enough to play a cello in a hotel for example.
My banjo mute is another heavy metal sort that clips over the bridge, that gives significant muting while preserving the quality of sound.