What I have read so far on the web is that there is no way to add a reserved IP to an existing VM (unless I recreate the VM which I am trying to avoid). However, I have noticed
For new VMs (with resource manager) you should do the following:
Create new static IP address:
$ip = New-AzureRmPublicIpAddress -Name "" -ResourceGroupName -Location eastus -AllocationMethod Static
Get information about VM Network Interface:
Get-AzureRmVM -ResourceGroupName -Name | Select -ExpandProperty NetworkProfile
Get corresponding network interface and set new ip and update NIC:
$netInt = Get-AzureRmNetworkInterface -ResourceGroupName "group-name" -Name
$netInt.IpConfigurations[0].PublicIpAddress = $ip
Set-AzureRmNetworkInterface -NetworkInterface $netInt