This page provides details on how to find four-socket Broad Swords, Crystal Swords and Long Swords in Diablo 2 Resurrected.
Finding runes is relatively straight-forward, either the monster or container you score loot from has a high enough Monster Level (mLv) or is located in a high enough Area Level (aLv) to generate a rune, or it’s not. General rule of thumb, the higher the difficulty/later the Act, the higher ceiling for rune drops.
Socketed equipment functions on a similar principle, but it can be less obvious, as the correlation between number of sockets in an item and rune rarity aren’t as clear. You can buy 3-socket weapons and shields in Normal difficulty, Act 2, so it may be reasonable to expect 4-socket weapons and shields to drop shortly thereafter. This, however, is sadly not the case.
Both 4-socket one-handed swords and 4-socket shields are desirable early-game primarily for the Spirit runeword, which has similar properties when created in a sword or a shield, namely +2 to All Skills, +25%-35% Faster Cast Rate, +22 Vitality and +89-112 Mana. With a relatively low level requirement of 25, you’re just not going to find anything better at the time, or in the cases of shields, perhaps not ever. Since the highest rune requires is Amn, it’s also not unlikely that you’ll find one just by playing through Normal difficulty, but failing that, Nightmare [Countess] will regularly drop them.
Getting the socketed base item, however, can take much longer, depending on your luck.
The maximum number of sockets an item can have is based on its Item Level (iLv) an invisible stat that’s usually the same as the mLv of the monster that dropped it (or the aLv of the container). In the case of 4-socket swords, weapons with sufficient iLv to spawn 4-sockets will not start regularly dropping until Nightmare difficulty. The only applicable base weapons (one-handed swords that can have up to 4-sockets) include Broad Swords, Crystal Swords and Long Swords (and the exceptional and elite variants thereof), although the latter are usually disfavored due to their Dexterity requirements (this shouldn’t deter a Paladin, however). Since an item’s iLv determines the maximum sockets and since Crystal Swords can have up to 6-sockets, we do not suggest having [Larzuk] socket a normal weapon - you might not get what you were expecting.
Instead, we recommend just picking up all socketed variants of these weapons you find in Nightmare difficulty until you find one with 4-sockets. We were unlucky and didn’t find one until Act 5, but on the plus side, doing [Eldritch] and [Shenk] runs in Nightmare difficulty caused them to drop fairly regularly, and it wasn’t long before we had a half-dozen specimens to roll. Nightmare [Cows] are also a great target for 4-socket swords.