Cast iron grills can impart the flavor. You need high heat under the grill pan and a way to vent the smoke. It's usually less intense flavor than comes from a live fire grill. The grill pans let the juices drip, then vaporize/char back up from the pan onto the item being grilled. A flat cast iron pan will not produce the same flavor, but the ridged ones are handy. I like the flat reversible grill/griddles better as i think they're more versatile.
There are flavoring cheats available as well, but require careful use and testing to get just the right taste. And without grill marks, the illusion can be broken. Liquid and powdered smoke for example. Many people decry these but they can add good flavors if used lightly and carefully. Smoked salt or paprika are more acceptable alternatives for most foodies looking for that hit of smoke flavor without the grill.
Also you can find Charcoal seasoning but that's pretty vile in my opinion, tasting more like ashes and burned than grilled.
You might also consider a Cameron Stovetop smoker. Similar foil pouches are available for one-off use. The Chinese do something similar with tea, rice and sugar in a wok, such as tea-smoked duck.