How to do it

The easy way

Wait for any outstanding aggression timers to expire and log off.

Drawbacks: you can't see anything or do anything with your ship.

The standard way

Fit and activate a cloaking device. You remain in space and can use scan probes you've already deployed.

Drawbacks: you can't activate any other modules while cloaked.

The ECCM way

Fit ECCM and Sensor Backup Array modules to your ship so that your sig radius / sensor strength < 1.08. Your ship will still show up on scan results, but people won't be able to get a 100% hit (i.e. one that they can warp to). You can sit at a safespot, providing gang bonuses, or do missions/complexes (with the risk of someone else probing out the complex, of course). It is also just about possible to hide a carrier, but you need combat boosters and a Ragnarok in the same system.

Drawbacks: you have to give up several low/mid slots to get the required sensor strength, and/or buy some expensive implants. Larger ships struggle with this method due to the number of modules required. Drones are easily probed out and should not be used with this technique.

How the ECCM way works

Game mechanics

Target size is calculated as sig radius / sensor strength. The smaller your ship's target size, the harder it is for people to probe you down.

There is a certain minimum target size below which it is impossible for anyone to get a 100% warpable hit on your ship. Without a 100% hit, people can't warp to you, and you're safe from being probed.

Multiple probes get up to double the % strength of hit of a single probe, so the worst-case scenario is when the strongest hit a single combat probe can get (operating at the shortest 0.5 au range) is exactly 50%. Working backwards through the scan strength equations gives the following formula:

Min. scannable target size = 5 / str_factor,

where str_factor is the product of all bonuses affecting the effective scan strength of the prober pilot (i.e. 10% per level of covert ops, rigs, sisters launcher, etc). For a covert ops prober with perfect skills, a full virtue set and Sisters equipment, this value is 1.08012498.

This may seem an ambitious goal for something as large as a battlecruiser, with a base target size of about 256/16 = 16, but there are some powerful effects that you can deploy to your advantage. A T2 racial ECCM nearly doubles your ship's sensor strength, and an ECCM Projector II gives the target a 120% bonus.

Example

A warfare-linked Claymore with max leadership skills & mindlink implant becomes totally immune to probes when fitting 2x ECCM II and targeted with 3x ECCM projector II. If the prober doesn't have an expensive Virtue set, or the Claymore pilot has Halo implants, it can drop one module and still be impossible to find.

So far, I've been very paranoid about potential probers. If your ship is only just above the prober's minimum scannable target size, you will still be extremely difficult to find. They will need near-perfect probe placement and hardly any scan deviation to get a 100% hit.

Resources

A spreadsheet which simulates different setups, taking into account all the effects listed below:

http://dl.eve-files.com/media/corp/KzIg/probe_immunity_v3.zip

List of things that can reduce target size

• Implants
  • Halo implants
  • Militia implant sets
    • Grail (Amarr)
    • Talon (Caldari)
    • Spur (Gallente
    • Jackal (Minmatar)
  • Skirmish warfare mindlink (when used with Evasive Maneuvers warfare link module)
• Modules
  • ECCM
  • ECCM Projectors
  • Sensor backup arrays
  • Evasive Maneuvers warfare link module
• Ships (that give improved fleet bonuses)
  • Ragnarok
  • Loki
  • Claymore
• Combat boosters
  • X-Instinct booster