Much of the techniques I use to boost martials are difficult to apply universally, but here are a couple.
1. I make efforts to give martials greater story focus
The fighter is one campaign took the noble background and the rest of the party were commoners. In a War of the Roses inspired campaign, that meant a lot of social interactions were principally with the fighter, even if the hard had better social skills.
In another Middle-Eastern campaign, the fighter was a fire genasi. Guess who was related to the overrarching villain. Also, being a fire genasi meant that they had to act as the face with respect to the many creatures they encountered who only spoke Primordial.
2. Spells sinks and environmental effects
I try to use environmental effects to make spellcasters use slots and to encourage multiple small spells rather than 1 encounter-ending spell.
When they spent several days on the plane of fire, the Wizard had to upcast (homebrew) Endure Elements at 3rd level on all non-fire resistent characters to avoid burning. This also cut down on the “every turn my owl familiar Flybys the monster to give advantage” because the wizard was unwilling to commit additional 3rd level slots on the familiars.
Also, casting non-cantrip spells in many places had a 1 in 4 chance of triggering a wild surge (my own homebrew table), thus making spellcasters more cautious with their high level spells.
3. “Yes, and…” and “No, because…”
I don’t like using this tool, but I still do on occasion. Unorthodox use of skills by anyone tend to receive a lot of slack. Unorthodox use of magic has me pulling out the spell description and 1) checking to see if anything is contraindicated; and 2) even if it isn’t, making an on-the-spot evaluation whether that use is “too powerful” for the level.
4. Standard “restrictive magic” rulings
Verbal and somatic components are clearly magic and cannot be disguised.
Casting a spell in a social situation without the consent of everyone present is akin to drawing a deadly weapon. People are likely to treat it like an active shooter situation. This even applies to spells like Tongues or Comprehend Languages, so you better communicate your intent before starting to chant ominous words.
Spell effects are obvious. Even mindless creatures affected by booming blade understand that they will take additional damage if they move. If a spell allows another creature to take an action to free an ally from the spell, the course of action and its effect is obvious to the creature.
5. Extensive use of non-spellcasting features
I try to ensure that racial features, backgrounds, skills and non-spellcasting class features come into play often and have a substantial effect.
6. Proficiency die (not yet implemented)
I’m considering using the proficiency die variant from the DMG for attack rolls, skills and saving throws, except that the proficiency die does not improve with level. Also implementing preset ways to increase your proficiency die in combat (such as flanking and magic weapons).
This should strengthen martials (because proficiency on attacks is relatively easy to increase) while reducing the consistency of spells (since saving throws tend both higher and more variable), thereby encouraging the use of more low-level spells, than encounter-ending high level spells.