Bungee w/ Hook - hooked to one side (the side of the broken cable) of the rear rudder mount arm. Paddlers who employ one of these bungee techniques typically leave the rudder arm cover off for easy access when a cable breaks. Make sure that the hook you attach to your bungee can easily be hooked to your rudder arm on either side. To deploy bungee - typically paddler will have to get in water or have a fellow paddler attach the hook to the rudder mount steering arm.
Deck mounted bungee - you can use a bungee on the broken cable side to restore steering that can be all be done with your other side pedal (* if you have installed this all before you launch *):
Well Nuts for Adding Mounts to Surfskis - or you can look for marine grade well nuts on the Internet or at your local hardware store - properly installed these are quite strong
Bungee looped around boat rear - another option is to carry a bungee cord with a hook on one end and looped on the other end that can be looped/anchored around the boat rear (instead of attached to a mount installed on the boat deck). Such a loop should be sized such that it will not slip and interfere with the rudder.
Jammed Pad - between the rudder and boat, aligning the rudder parallel with your boat so the rudder acts like a skeg or keel and at least contributes to going straight and reducing side slip and/or unwanted turning. Steering will then be primarily accomplished with your paddle (practice is not a bad idea). Carry such a pad on your boat or person - rubber, silicon, something with a little flex and not so hard that it will damage your boat but sturdy enough to stand up to extended time in the water. Test your choice of pad to make sure it will keep your rudder in a fixed position in rough conditions.
Broken Paddle (paddle clamp breaks, blade is damaged or falls off) You may prepare yourself for breaking your paddle by practicing paddling with half your paddle. Store half your paddle on your aft deck and paddle with the other half. Practice in progressively rougher water
Swimming - practice can help you determine what techniques are most effective under various conditions. You may have to abandon your paddle also in order to swim more effectively if there is little or no prospect for recovering your boat.
with paddle - If you are very bouyant (such as when you are wearing a dry suit) You can float on your back and back stroke with your paddle
Or hold your paddle just below the blade and point it in front of you and swim with your other hand.