Micro-switch inductive switching (DC)
The time constant is indeed L/R, where L is the inductance and R the resistance of the circuit. This value is important because it sets a limit on how long it will take for the arc to extinguish when the switch contacts open.  

So why not simply specify a maximum inductance? Many loads such as relays, solenoids, and motors have an inductance which varies depending on what they are doing, and few have the value stated in their specs. Measuring in-circuit inductance directly is often difficult, but it can be roughly estimated from the length of time it takes for the current to decay. And since that is what we want to know anyway...  

An inductance of several henries might seem unrealistic, but is not unusual for a large electromagnetic device. For example the Panasonic S4EB-48V has a coil inductance of 3.41H - and that is just a small relay.

If you are worried about arcing contacts due to a highly inductive load, simply put a diode across it in reverse. When the switch opens the diode will immediately become forward biased by the back-emf and maintain current flow until it decays, without allowing a dangerous voltage to build up.