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ORIGINAL: AndrewJ
It depends on what sort of wire guidance your missile has.
If it's a MACLOS (Manual Command Line of Sight) system, where the operator visually identifies the position of the missile and manually flies it towards the target, then there is little that can be done other than shrouding the target in smoke, or relying on optical dazzlers to blind the operator. These dazzlers are typically laser systems, such as the cancelled American Stingray, which was mounted on a Bradley, or the dazzler mounted on some recent Chinese tanks. If the operator is using magnifying optics then they would be more vulnerable to these systems than an operator using the naked eye. However, since the laser systems generally project a relatively small beam, it is important for the targeted vehicle to identify the exact location of the missile operator in order to illuminate him.
If it's a SACLOS (Semi-Automatic Command Line of Sight) system then there are more options. Smoke and optical dazzlers would still work to defeat the operator, but there are also ways to jam the tracking system. Most SACLOS systems use a set of optics on the missile launcher to track some sort of flare on the rear end of the missile. If the tracker cannot properly identify the missile's flare then it will send wrong guidance commands, causing the missile to miss. Powerful modulated infra-red sources (such as the Russian Shtora, or equivalent Chinese or Western systems) or decoy flares (such as available for the French Galix system) have been fielded in order to 'fake out' the tracker on the anti-tank missile launcher. This type of jamming is easier to apply than dazzlers, because the defender does not need to find the exact location of the shooter. So long as the jammer is in the field of view of the tracker on the missile launcher it should be effective. Later SACLOS ATGMs started using more sophisticated systems with special coded strobes in order to help the tracker distinguish the missile flare from false targets and interference generated by these systems.
If it's an imaging system, where the wire guidance is usually a fibre optic link transmitting a video image from the nose of the missile, then that sort of jammer will not work, although IR smoke and dazzlers directed at the missile might do the trick.