There is no real Swift replacement.
You can check in the following way:
someObject.someMethod?()
This calls the method someMethod only if it's defined on object someObject but you can use it only for @objc protocols which have declared the method as optional.
Swift is inherently a safe language so everytime you call a method Swift has to know the method is there. No runtime checking is possible. You can't just call random methods on random objects.
Even in Obj-C you should avoid such things when possible because it doesn't play well with ARC (ARC then triggers warnings for performSelector:).
However, when checking for available APIs, you can still use respondsToSelector:, even if Swift, if you are dealing with NSObject instances:
@interface TestA : NSObject
- (void)someMethod;
@end
@implementation TestA
//this triggers a warning
@end
var a = TestA()
if a.respondsToSelector("someMethod") {
a.someMethod()
}