You have still have not provided any information so that we know what current you are trying to switch. You say that you can't measure the resistance but did not give the reason. Is the resistance so low that it is below the range you can read with your meter. Here are some suggestions to measure the resistance.
1 - Measure current taken by the electromagnet when connected directly to the 12 volt supply.
2 - Connect a resistor in series with the electromagnet and connect it to the 12 volt supply. Measure the voltage across the resistor. I suggest starting with a 10 ohm resistor. We may suggest changing this depending on the result of the first test.
3 - This method will only give us a very rough idea of the resistance. Post some pictures of the electromagnet and any information you have such as manufacturer, part number, supplier, Ebay advert where you bought it. Measure the wire diameter, the length of the winding, the outer diameter of the winding the inner diameter of the winding. From this we (Or you if you are prepared to make the effort.) can calculate the rough length of the wire and the resistance per unit length of the wire and hence the resistance. As you have been told a number of times we can't specify a suitable switching device and possibly the amount of heat sinking it may require without some information.
Les.