[Griefbringer]

I would like to second the comment about using light indirect fire, especially the smaller calibre infantry and field guns (around 75 mm) available in many armies can be handy, as these cause limited damage (less danger to your own troops) but plenty of suppression.

Light and medium mortars (up to 82 mm or so) also cause a plenty of suppression, but are also more dangerous to infantry, so be careful with hitting your own lines. However, they are not much of a risk to armoured vehicles (HE Pen 1), so you may try to keep a few tanks just behind your infantry line, where they can provide immediate response if enemy is encountered.

When pounding positions close by, try to make sure that spotters have LoS - otherwise there is much greater risk of the fire drifting to your own lines. Sometimes smoke from the bombardment can cause the observer to lose LoS, so do not lay the barrage too thick. Also, it is better to use on-map artillery rather than off-map artillery for this kind of missions, as off-map artillery can sometimes lose communications and keep on pounding position that you don't want it to pound anymore.

For something less sophisticated, there is also the "recon in force" approach of sending in cheap, expendable infantry (e.g. Soviet penal company) moving quickly to locate the enemy line - they will take casualties on contact, but should be able to retreat relatively safely due to close terrain. While they try to rally, actual combat troops (with artillery support) deal with the enemy, and then the more expendable troops move to the fore again advance continues. Not exactly my favourite tactic, but in campaign settings I prefer to lead my advance with some expendable auxiliary units.