For the purpose of this question, assume "two weapons" to include "a one-handed weapon and a shield".
Compared to other spellcasters, Eldritch Knights are sort of at a disadvantage when it comes to achieving dual-wielding and the like, as they generally cannot use spellcasting foci (except when using magic items such as a Ruby of the War Mage). Thus, they normally seem to require a free hand for casting spells with components other than verbal ones. For comparison, a wizard could wield a Staff of Power, which – due to being a staff – counts as an arcane focus and thus solves the issue of noncostly material components, but it can also be used as a +2 quarterstaff.
For an EK trying to trivialize somatic components, Warcaster is the obvious choice (no difference to other spellcasters in this regard), and the requirement of a free hand for material components (without a GP cost) can be avoided with a Ruby of the War Mage. However, the former requires spending a feat (even though Warcaster is a pretty good feat for EKs anyway, especially considering that fighters get more ASIs than the average class), and the latter blocks an attunement slot and doesn’t work for costly material components. Plus, if you happen to die in a battle, your attunements end, even if you get Revivified right away (although that’s probably a very rare or even legendary problem ^^).
Is there a cheaper way to get around the issue? For the purpose of defining "expensive", please consider this order (the higher up on the list, the more expensive):
- Multiclassing (and requiring three multiclass levels is obviously worse than requiring one)
- Requiring additional actions
- Attunement Slots
- Requiring additional bonus actions
- Choosing specific (sub-)class options, such as a Fighting Style.
- Magic Items without attunement
- Ingame time (e.g. downtime training)
- Requiring your object interaction
I’m aware of other questions on almost the same topic, namely this one (warlock-focused or at best generic), this one (technically answers the issue, but some GMs might consider dropping and picking your weapon up cheesy, plus there are downsides and it only works with Sage Advice rulings), as well as this one (answers claim it’s not an issue, which is not true IMHO – for example, Booming Blade or Green Flame Blade, both great melee cantrips for an EK, have material components).