They did use shields in sieges - but large pavises to hide behind.

And almost all of their military weapons were two-handed: katanas (which can be used one handed but less effectively), naginatas, long spears, bows, staffs, huge tetsubo clubs....

In any case in the earlier Heian and Kamakura period the samurai were primarily horse archers anyway and used a box-like form of armour with large shoulder pieces which did to some degree provide shielding but made it impossible to use any hand-hand-to-hand weapons other than a dagger - which is why most of the combats in the Heike Monogatari take the form of horse archery duels ending with grappling and a dagger stab.

While later Ashikaga and Tokugawa period armour is much more practical they switched primarily to long spears and katanas - and then eventually to firearms.

The Chinese and Koreans from whom they acquired much of their military technology didn't make much use of shields either - being similarly devoted to the use of two-handed polearms, bows and crossbows.