Decades ago, I shot Black & White film. Recently, I have started shooting color with a digital camera that looks like my old 35mm camera. In the old days, if I was uncertain of the best exposure, I would bracket either the time or the f-shop. As a roll of B & W film was limited in the number of shots it would take, I would just pick 2 shots rather than 3. I think it was better to shoot once at the exposure the camera's meter recommended and the other, one stop above, to overexpose. I had a friend who was a professional and I think that he recommended a small overexposure rather than a small underexposure. This was some time ago.
Maybe I should just rephrase this. If one is slightly uncertain of the best approximate exposure should one, over or under, expose.
The underlying technology varies quite a bit between film and digital. The exposure strategies that give the best results for film may not give the best results with digital. A fundamental difference is the shape of the "response curve". With film, it has an "S" shape, and with digital it's more of a straight line. With film you need to hit the midpoint of the "S" (where the curve approximates a straight line). With Digital you can hit anywhere on the line. With film "Over-Exposure" means you have missed the center of the "S", and you are not getting the nice straight-line response. With Digital, a higher (or lower) exposure isn't a problem.
"Exposure" is the term we use to refer to the amount of light hitting the sensor/film. Usually, this is measured in terms of light per unit area. Exposure
does not refer to whether the image is too light or too dark. An over-exposed negative can be printed as a dark, light, or normal print.
With digital, the term "over exposure" is typically used to describe a situation where there is a mismatch between the ISO setting and the exposure. Unlike film, this doesn't necessarily mean the exposure was too high, it might be the exposure was perfect, but the ISO was set too high. With digital the term "Over Exposure" can frequently be replaced by the phrase "ISO set too high".
With this viewpoint in mind, we can rephrase your question as to whether it is a good idea to set the ISO a little too high or a little too low for a particular exposure. When you look at it that way, you can see that there are options not practical with film.
One strategy for getting the best digital results is to decouple the exposure from the ISO setting.
The first step is to maximize exposure, this helps minimize image noise, and helps preserve shadow details. Get as much light as is practical on the subject. Choose the widest aperture that gives you sufficient depth of field. Choose the slowest shutter speed that doesn't yield objectionably motion blur.
Then you set you ISO. If you are worried about losing highlight detail, use an ISO setting that's a little lower than what your meter recommends.
Remember, with digital by varying your ISO setting, the same exact exposure will be called "under-exposure", "over-exposure", or "good exposure".
Shoot in RAW to give you the widest latitude to adjust image lightness when you process your image.
Another option with digital is to continue with manual Aperture and Shutter as above, but use Auto-ISO. If you are worried about blowing highlights, use negative "exposure compensation" to get the camera to choose a slightly lower ISO. Keep in mind that not all cameras allow "Exposure Compensation" when shooting in Manual Mode and Auto-ISO.
Note: "Exposure Compensation" (EC) simply sets a bias on the camera's metering system. The name is leftover from the days of film, when biasing the meter would change the exposure. On modern cameras EC might change the exposure, but it might also leave the exposure the same, and change the ISO.