The rules state:
Saving Throws: Nonmagical, unattended items never make saving throws. They are considered to have failed their saving throws, so they always are affected by spells. An item attended by a character (being grasped, touched, or worn) makes saving throws as the character (that is, using the character’s saving throw bonus).
Magic items always get saving throws. A magic item’s Fortitude, Reflex, and Will save bonuses are equal to 2 + one-half its caster level. An attended magic item either makes saving throws as its owner or uses its own saving throw bonus, whichever is better.
and in addition:
Voluntarily Giving up a Saving Throw: A creature can voluntarily forego a saving throw and willingly accept a spell’s result. Even a character with a special resistance to magic can suppress this quality.
Usually a harmful spell allows a target to make a saving throw to avoid some or all of the effect. The Saving Throw entry in a spell description defines which type of saving throw the spell allows and describes how saving throws against the spell work.
So, lets break this down. In terms of attended objects, we have two cases. The first is the case where the item is saving 'as the creature' and the second is the case where the item is saving as itself.
Now, the usual method of voluntarily giving up a saving throw clearly doesn't apply in a prima facie manner, as objects are not (with a few exceptions) creatures. However, in the case wherein an item is saving as its attendant, it seems this rule might end up applying. The rules indicate that 'makes saving throws as the character' means the same thing as 'makes saving throws using the character's saving throw bonus', but that still isn't entirely clear.
Since the plain readings of these phrases do not align in meaning, the GM must determine whether anyone using the character's saving throw bonus to make a save is 'saving as the character' (and thus can voluntarily fail the save as if it were a creature, make use of consumable bonus effects such as is granted by resistance or re-roll granting effects such as is granted by the Charmed Life feat) or whether, instead, anyone 'saving as the character' merely uses that character's saving throw bonus without accounting for any other effects or features (and thus all abilities allowing another creature to use your save(s) would disallow the use of such abilities on the roll).
Now, were this the only consideration, an attended item using the attendant's saving throw could choose to forgo its saves voluntarily, if it so wished, provided one of two possible interpretations of an ambiguous passage is taken to be the case (in the other interpretation they would not be able to do this). Magic items using their own saves, were this the only consideration, would be unable to forgo the throw, since they are not creatures, but it is important to note that the phrase 'whichever is better' does not mean 'whichever is higher' and so a magic item would essentially get to choose voluntary failure anyways, since it would use the more preferable of the attendent's and its owner's rolls to count as a creature, were access to voluntary failure better for it than success.
This is, of course, not the only consideration.
The text describing what it means for a spell to allow a saving throw in the first place makes it clear that spells with listed saving throws allow their targets to save. This wording indicates that all saving throws made pursuant to that section are entirely optional. You are allowed to make a saving throw when spell says so, but nothing says you have to do so, even if you are an object rather than a creature. Indeed, the 'Voluntarily Giving up a Saving Throw' option is an additional option available to those called to make a save who happen to be creatures.
In some interpretations of what it means to forgo a save, these options are identical. In others, the difference between choosing to take your saving throw but then forgoing it (as is allowed of creatures) is significantly different from choosing not to make a save in the first place. An example of the possible impact of exercising the creature-only option as opposed to the general option can be found here, and an explanation of the different interpretations of the relevant passages which lead to the differing systems here.
Putting it all together, then, the situation is as follows:
An attended item can choose to take (or not take) a saving throw as its attendant when a spell indicates it would make a save. If it chooses to take the saving throw, it may or may not (as a matter of rules interpretation) be able to forgo the save as if it were a creature making use of the 'Voluntarily Giving up a Saving Throw' rules, provided it is attended by a creature. A magic item must save using its own bonuses, if that is best for it, or by saving as its owner, if it chooses to save. If items saving as creatures get access to the 'Voluntarily Giving up a Saving Throw' rules, then Magic Items gain access to those rules just like regular attended objects, except that when choosing to save using their own bonuses they do not have access to that section of rules if they are not a creature.
Thusly, items can choose to forgo their saves, but possibly not quite in as many ways as creatures.
Note that, in any case, it is the item that is potentially permitted to forgo the saving throw, and not the item's owner or attendant, who possesses no special powers related to coercion of the item's consent simply by virtue of ownership or attendance.
"But objects can't make choices or want things!"