PowerShell script to retrieve the public X509 certificate from a remote TLS endpoint

Get-RemoteSSLCertificate.ps1

[CmdletBinding()]
param (
    [Parameter(Mandatory=$true)]
    [string]
    $ComputerName,

    [int]
    $Port = 443
)

$Certificate = $null
$TcpClient = New-Object -TypeName System.Net.Sockets.TcpClient
try {

    $TcpClient.Connect($ComputerName, $Port)
    $TcpStream = $TcpClient.GetStream()

    $Callback = { param($sender, $cert, $chain, $errors) return $true }

    $SslStream = New-Object -TypeName System.Net.Security.SslStream -ArgumentList @($TcpStream, $true, $Callback)
    try {

        $SslStream.AuthenticateAsClient('')
        $Certificate = $SslStream.RemoteCertificate

    } finally {
        $SslStream.Dispose()
    }

} finally {
    $TcpClient.Dispose()
}

if ($Certificate) {
    if ($Certificate -isnot [System.Security.Cryptography.X509Certificates.X509Certificate2]) {
        $Certificate = New-Object -TypeName System.Security.Cryptography.X509Certificates.X509Certificate2 -ArgumentList $Certificate
    }

    Write-Output $Certificate
}

I modified my copy of the script to write the certificate to file with:

$CertExportDirectory = 'C:\temp\'
$CertExportName = $ComputerName + '_Port' + $Port.ToString() + '.cer'
$FilePath = Join-Path $CertExportDirectory  -Child $CertExportName
Export-Certificate -Cert $Certificate -FilePath $FilePath

With output like "C:\temp\example.com_Port443.cer"

I also run a validation check with:
Test-Certificate $Certificate

You may want to set some of the non-default Test-Certificate parameters depending on use case.

Any ideas how to adapt this for retrieval of the certificate used by a remote SQL server (i.e. port 1433)? The script hangs at $SslStream.AuthenticateAsClient('') when I try to use it this way.