I've always used the Moq Setup method. So your first example would become;
var push = new Mock<IPushService>();
push.Setup(a => a.SendPushNotification(It.IsAny<UserDevice>(), It.IsAny<string>(), It.IsAny<int>(), It.IsAny<string>()));
Likewise your second example, which is working anyway, would be as follows (notice the returns which I assume is a bool)
var mail = new Mock<IEmailService>();
mail.Setup(a => a.SendMessage(It.IsAny<string>(), It.IsAny<string>(), It.IsAny<string>())).Returns(true);
mail.SetupProperty<bool>(a => a.ThrowErrors, true);